Meep I suspect you have landed up in a department that is unused to PhD students. This might mean supervisors who have little supervisory experience, no dedicated administrators and few PhD colleagues / training opportunities. While this can be a chance to be a big fish in a small pond, and some have thrived in that environment, it sounded like you'd really benefit from a larger PhD community, organised graduate school, experienced supervisors etc as that would give you the atmosphere you were hoping for. Are there any other universities that would be geographically viable? Does your current university have any doctoral training partnerships with other institutions? Sometimes cross-institution supervision can be managed in those circumstances.
If the answer to those questions is no, I'd suggest making an appointment to see whoever formally has responsibility for PhD students in your faculty (a dean or similar) or failing that your HoD. Explain what has happened - go in with a long list of issues. Ask about changing registration from distance to p/t and ask if they'd give you a workspace if that happened (being seen regularly in a dept even a disorganised one) can help.
But if I'm honest, if it's possible I'd leave and restart somewhere else.

How have you ended up as a distance student when you don't want to be one?? Is there a Facebook PhD student page for your uni - maybe that could help you make some contacts and get some answers. I was a distance learning student but I was given a lot of attention when I started - this is when they should be bending over backwards to show you how you can contribute to your department even if you are not physically there. I would be very worried.

Thank you very much, everyone, for your thoughtful and informative comments. I have read them all.

I think that at this point in time, I have had a bit of a knock to my confidence and I am fairly busy in work as well. I think I may withdraw but look to sign up elsewhere next year or the next year. I am comforted by your comments that it was not meant to be like this. I look forward to hopefully having a break and a less frustrating time.