i think i can help with a few of your questions
the type of visa needed will be a fiance visa- very similar to the spouse visa apart from the fact that you need to marry her within 6 months of her getting the visa an coming to the UK, then apply for the 2yr ILR
i dont think thats its a prerequisite that you have 2k savings but it helps
with accommodation- get a letter from your landlord and a few pics of the place- that should be enough, no need to really mention that its a shared house
with regards proof of relationship- anything that can prove how long you have known her- not just pics should be enough proof. i think that you need to have known each other for a minimum of 9 months but i am not 100% sure on that one
one thing that a wise old chap once told me was you can never have enough info- if in doubt then just include it in your application- noones ever had a visa refused cos there was too much info supplied but many have cos there wasnt enough
