Oh I really do understand. Talking about difficulties with strangers can be excruciating and very upsetting. I can hear that its stressing you out already. Try not to worry too much. Its absolutely normal to cry or to be nervous. No shame in it at all and the assessor will be experienced and is on your side. No one will be trying to trick you or say you don't need this or that. The main thing is that everyone does want you to have the support you need so as to make university successful and fun for you. However even if it did all go wrong for any reason then you can appeal.
I know you want to be more independant but you don't want to put strain on yourself either. The more support you have with study then the more you'll be able to cope and maybe do new things too. If you find you don't need all the support as time goes on then you don't have to have it. So if you had a mentor/support worker then YOU decide how best to use them and whether to continue with them. If you don't get one in the first place it might be harder to arrange later. So have a think as whether its best to try to get a support worker to start you off at least.
Those are the exact kind of things you need to say.
1. Public place issues. You need to work in your room at lot and research/read there. So some ideas would be: access to internet, a computer of your own as you cannot easily access the public/shared computers, a printer of your own. Extra money for photocopying and to buy your own books, ink/paper allowance.
A support person/mentor to help you when neccesary.
2. Motivation: A support worker or mentor.
3. Tiredness/concentration issues: extension times for essays/course work/extra time in exams/use of a word processor in exams if your handwriting speed is affected/ early lecture notes in advance/lecture notes to be provided (can all be arranged with the university themselves). A recorder for lectures which you can use or give to a friend at times when you may not be able to attend. Voice recognition software and reading programmes for your computer so you can listen to text rather than have to read it all.
Everything on the list the person above posted.
4. Course specific help... depends what you are studying really.
These are just ideas and you may have some of your own. Don't forget if you don't want or aren't allocated a support worker then the university itself will have some help available in their access centre to help plan and sort out work with you.
You're going to be fine. Honestly. The fact you've got this far speaks volumes for how brave and determined you are to my mind.