Personally, I would never consider an unfunded PhD. I can't think of any scenario where this is a good decision. Academia is overcrowded (there were already nature issues about it ten years ago and it became rather worse than better) and if you can't secure funding, it is unlikely that your CV is competitive enough to land an academic post after your PhD. Not saying that it is impossible, but very unlikely. Many people are flattered when a professor, sometimes leading in the field, is keen on supervising them but seriously, you are just free labour. In the lab sciences it is pretty common to hire PhD students from China or India just because they are coming with their own government funding and do not cost anything. Why wouldn't you agree if someone offers to work for you for free? Keep in mind that the professors with a great reputation are seldom the ones who have a lot of time to spent on supervision. A funded PhD is no guarantee for success afterwards but at least you are not in debt. There are btw also many options abroad. There are tons of international PhD programs in English all over Europe.

Definitely the funded one. I would never do an unfunded one. It is just not worth it. Big job opportunities after the PhD are rare, so you should not take the risk. Universities and supervisors are just exploiting you. Rankings are overrated. If you publish great stuff it will be recognised ;) It is also much easier to produce good work if you don't have to worry about money.

It depends on your field. In most cases, a PhD will make it even harder (!) to find a job afterwards. You are highly qualified and there are only a few positions that require this expert knowledge. That's why so many PhD graduates work out of their field afterwards. There are however some fields where it can be beneficial. For instance, if you want to work in an industrial research facility as a chemist, they might want someone with a PhD.
I agree with TreeofLife, do the PhD only for the sake of doing a PhD or because the career path really requires the PhD. If the job you are going for can be done with a master degree, the PhD degree will rather lower your chances on landing a job. They see you as overqualified.

A new language will probably not help you to find a job so I would not do it for that purpose. There are only few jobs where speaking an additional language is more than nice to have. They hire you for a specific function in a company and unless this function is translation, it is going to be not that beneficial. Not mocking this at all, it is great to speak different languages, I am actually thinking about learning another one myself, but in terms of jobs languages are vastly overrated. Most employees that deal with international customers have to speak English.

In terms of learning it fast, I would do language courses until you have a basic level and then continue with these "tandem-things" (maybe they are called different in the UK), where you meet with a Chinese that wants to improve his or her English and you speak with each other. One Chinese PhD student in my lab is doing that to learn German. Doesn't cost anything and is really efficient. I think mandarin is too complex to learn it on an online platform. Good luck.

Well, first of all: As a foreigner, I would not pursue a PhD in the UK unless you get an exceptionally nice scholarship. I hope that is not seen as offensive by UK users. The research is often top notch but there are a lot of other countries with equally good research facilities and way better conditions for PhD students in terms of salary and funding duration. Oxford, Cambridge or Imperial College might be an exception but also hard to get in. At most Universities you get an average salary for 3 years and then you are on your own, while in many other countries the salaries are decent, 4 years funding are standard and you are a full employee , which means you can get unemployment money in case you run out of funding (in my case 70% of my salary). But the research is of course cutting edge and some of their Universities are in the top ten worldwide ;)

If you want to work in industry, a PhD in industry is in my opinion always preferable. You show already before your PhD that you are interested in industrial applications and I guess that the chances are high that they hire you afterwards if they were happy with your work. However, that is probably highly company dependent and depending on the University you are working with that will award the PhD eventually. I think the question is also if you can secure a PhD in industry as there are not that many as far as I know. I am however not a chemist. Maybe there are more opportunities than for biologists :)

Good luck

You can always try "nature jobs" or similar websites. When I was looking for PhDs, I frequently looked on nature jobs and found that most of the new PhD positions in natural sciences were advertised there. I think however that this will be difficult. Majority of post docs are either paid by a fellowship or they got the position over connections. For one of the open post doc positions in my lab they had over 300 applicants and I was told that this is pretty much standard today. Some positions are only advertised because they are obliged to advertise it, even though they already have someone for the position. I guess you need an opening in more or less exactly the specialized field you did your PhD in to be competitive. But as applying doesn't cost anything but time, you can always try. Maybe your supervisor can pull some strings or knows some people in your field that might need a postdoc in the near future. That's probably the most promising way to find a position.
Good luck!

Why do you have to buy a house in the new state or why did you even buy one in Texas? Can't you just rent a house for that period? What if the job you get after your post doc is 200 miles away from your house? In Germany, you would never ever get a loan with a temporary contract, but that's probably not helping...I was just curious