I went from student to unmarried partner, but I am not an immigration expert, so please verify things!
1. I did my application in-person and I didn't have to show any information about the end of my student period. I officially finished the degree in June, hit the two-year living-in-sin mark in October, and switched in January, with a visa expiring in February. I don't think you should have a problem with the length of time remaining on your student visa (did they think you were finishing the degree much later than you actually did?) but please check with someone who can confirm this.
2. I don't think it would be a problem. Presumably you can show that wherever you have been living in the previous two years, you have mail addressed to both of you - if not jointly, then at least at the same address. If you have a joint tenancy agreement for the sublet, I suggest using it as part of your evidence.
3. It used to be 20 documents. It's now 6. So you probably ran into older information somewhere.