Your boyfriend gets housing benefit because he gets high rate care DLA. You would get nothing at all renting from a family member.
If you rented from someone else you would only be allowed one bedroom rate as you are a couple and expected to share, and it would very likely not pay the rent - look on the local council site or go here
https://lha-direct.voa.gov.uk/search.aspx and put in one bedroom and a local postcode it will tell you.
Don't forget DLA is changing to PIP this year. You *really* need to contact someone about doing that as the criteria is much much stricter than DLA and you may lose your low rate you now have - please contact CAB before reapplying.
With the carers allowance, how do either of you expect to be able to claim that and get mid/high care yourself, or have I missed something? I don't mean to sound rude or anything, but you have mentioned some fairly serious issues you have so how do you expect to function as a carer for someone else? It may be seen as fraud and a reason to remove a DLA award altogether.
Council tax where one person is a student and the other works is 25% reduction on the bill, council tax benefit will not pay the remainder.
There is a benefits calculator which may help you calculate how much you can get which is here
http://www.turn2us.org.uk/benefits_search.aspx though your boyfriend being a student makes things a bit complicated.
Final thing, you can try another CAB!
I hope this helps and isn't too confusing!!!