Everyone I know who had decent supervisors went through this. It's only when they read a full draft that they read the argument in full and can see the gaps / problems. If you think about it, if you only read one chapter of a book then your ability to critique the whole thing is limited. They are also now reading with the knowledge of who is going to examine it - knowing the quirks of the examiners can also make them think you need to add a bit to forestall a predictable question. Don't let it get you down, just try and respond as best you can.

I can't say anything about the US but I think there's a similar forum to this (possibly called gradschool cafe) that would probably be able to help on US applications and your chances.

Within the UK, it's not clear from your post whether you would be aiming at ESRC or AHRC funding. I think with either though, it's so competitive that you would be stupid not to apply everywhere that has allocated funding for your area and a suitable supervisor. I think your supervisor at the MA university would understand that.
Your experience in the country will be a plus (spin your networks, knowledge of sources etc as much as you can) but the 2:1 is going to be an issue (because it's so competitive there are lots with 1sts applying) and I would suggest that if you were unsuccessful in the next funding round, but were then awarded a MA distinction, that you didn't rule out a reapplication in 2014 with the distinction in hand, as I think it might make a difference. I'm assuming your Spanish is fluent - if so and it's ESRC that covers your topic, you might want to investigate which doctoral training centres were awarded specialist language-based area studies funding for Spanish / Latin-American studies. I understand that these studentships have to be awarded but because of the language requirement are a bit less competitive than straight politics. The info is on the ESRC website.
One other thing that I would suggest - if getting funding is hard, getting an academic job is even harder. Make sure you know from the beginning what it takes to be competitive on the academic job market (and the realities of what the job is like) and have a plan B that is feasible. Both Politics and History produce far more PhDs than there are academic jobs, and unless you're clued up from the beginning and also keep other options open, then it can all end in tears.
Hope this helps and sorry if it sounds discouraging.

Marasp - I'm social sciences so it may be different but I don't think so. In my field at least, this sort of thing shows that you have networked, which is good, but is not as important as REF-able publications. I was told to concentrate my efforts on those rather than anything else as they are the filter that is used to decide who to shortlist.

I wouldn't worry about how it looks on your cv - a lot of people are in the same position. Use your cover letter to explain why you want the job though - training in a particular skill - so that it makes sense to the people reading the application.

I think it would depend on how the project has been designed as to whether you'd have any chance or not. If they have committed to certain types of data analysis and collection, then you would need those skills and while you can get training on how to use a particular software package, you couldn't realistically pick up quant skills to a reliable standard from nothing very quickly (particularly if the last maths you did was GCSE). Did you have any methods training as part of your PhD? If so, I'd emphasise anything even vaguely relevant.

It's rather odd to contact your supervisor and not you. I think I'd phrase it as 'initial interest' rather than anything more substantive in an application. But I'd agree with Larrydavid about checking first whether it is a reputable firm. In addition to those he mentions beware of Lambert / HDM or any of their numerous names based in Saarbruecken in Germany. they even got caught 'publishing' wikipedia articles and selling them on Amazon...

I know someone who did this but it was some sort of marine biology thing where NZ was the ideal field location and the centre of excellence. He seemed to enjoy it and thought it less pressured that what friends were experiencing elsewhere. He's still there so clearly it worked for him. The biggest downside was isolation from the scientific mainstream - it costs a lot to get to the important conferences, and it's not as easy to network. THat would be a downside perhaps if career wise you wanted to return to Ireland afterwards.

Is there any chance that you could apply to defer the start of the funding for a semester to give yourself a little longer to recover? I'm assuming you'd be able to get a letter from your doctor to confirm that you have health issues, and given your subject, I would imagine that the supervisor would be understanding, if the conditions of the funding allow for it. The other thought I had was that maybe it would be possible to contact the student wellbeing / counselling service now, and get some advice from them about what support could be put into place for you so that you didn't feel as if you were stepping into the unknown without any back-up.
In some ways although it seems scary, maybe starting something new would actually be a positive experience for you. How convinced were you that a PhD was right for you before you became ill? If you were really keen, I think I'd be inclined to go for it if the idea of deferring doesn't appeal. But it's hard to advise you as what's right for one person isn't for another. Similarly, yes doing a PhD is challenging and some find it very difficult to cope. But there are other posters on this board who have successfully completed PhDs despite having similar problems to yourself before they started. You might want to do a search for Keenbean's posts for an example of success as s/he is also in pyschology.

Not unless you readminister them so basically start again. If you change the questions but use the responses to the previous set of questions, then your data would not be valid. Doing so could land you in quite a bit of trouble. Unless you have time to start again (and a pool of respondents that are willing to fill them in again) I think your best option is to tell your supervisor that you've already got the data, and is there any alternative types of analysis you could do on it, that might help to meet their concerns about the original questionnaires.

I think it's not so much getting a place (although I think you'd be unlikely to get a place at Oxbridge tbh from what I have heard from other people) that is the problem.The problem is that you are very unlikely to get funding for such a competitive subject anywhere without an immaculate academic track record these days, let alone at a top university. Unlike in the sciences where people with 2:2 degrees are still getting funded, humanities funding is so scarce that it's unbelievably competitive.
Self-funding a PhD is very risky (for most people - obviously if you have a trust fund or a wealthy partner this might not be the case) and something that you should only do with your eyes wide open to the realities of what doing a PhD is like, and an understanding that very few people who complete a humanities PhD will get an academic job (and as Angelette points out that it can be disadvantageous in a non-academic job search). There's quite a good chapter in Phillips and Pugh's book 'how to get a PhD' on the reasons why you should and shouldn't do a PhD, that would be worth reading. Academia is pretty cut-throat, as the many deeply disallusioned posts on this forum will show you, and doing a PhD without funding is IMHO only worth it, if you have such a passion for your thesis topic that nothing else will make you happy than to spend (assuming you go part-time like most self-funders) at least the next 6 years of your life researching. http://chronicle.com/article/Graduate-School-in-the/44846/ US-focussed but might be worth a read as many of the problems described are the same here.

http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=420451&c=1 an update.

I'd say that job market in the US is less competitive that it is in the UK at the moment as in my field, you can still get jobs there without publications which isn't the case in the UK. To be competitive for a UK job atm you need to be able to be submitted to the REF, have teaching experience and a viable research agenda post-PhD. Oh and the ability to deliver on the REF impact agenda. It might help to be able to walk on water too ;-) Lots of publications in less REF-worthy outlets are not helpful but you are expected to have done some conference presentations. One big difference I can think of between the UK and US is that where you did your PhD and who your supervisor was is a lot less important than in the US.
You just can't generalise about Europe. The hiring process varies a lot between countries but in general you are expected to have more publications than seems to be the norm in the US.

That's surely bordering on the illegal. I hope someone reports them for violating NMW legislation, but I have a horrible suspicion that they could spin it as free training even though it looks like a job to me. I thought some of the temporary teaching fellowships were bad enough forms of exploitation but this really is awful. And the true shame of it, I bet they will get lots of applicants.

To avoid the problem with references in the future, a suggestion might be to have a paper handout of your slides, so that rather than having to flick forward on the screen you can refer them to the handout. Was this some kind of progress review as you speak about examiners? If so, you should get some written feedback, which might help clarify the oral feedback they gave - sometimes straight after a stressful presentation, I think we all tend to overreact to criticism simply because we are wound up and any criticism feels both harsh and unfair. It might be that it's not as bad as you think right now. Were your supervisors there? If so, ask them for feedback too. But before asking for or reading any feedback, have a couple of good nights' sleep first and do some nice things to take your mind off it, and then when you're refreshed tackle it.