Immediate help required - Proof of Accomodation for dependant visa

I would appreciate it if someone could guide me on my queries about providing proof of accommodation while applying for a dependant visa.

Context

I am a first-year PhD student and joined my University in Oxford in January 23. I plan to bring my family here on a dependant visa in November 23, including my wife and 3 kids (son - 11, daughters - 8 and 6 years). For proof of accommodation, I am doing a tenancy contract with my cousin for renting his home in Birmingham (2 beds, 2 toilets,1 living room and Spam), I'll have the complete house all to myself. I'll be coming to Oxford once a week as remote work is also possible due to computer-based research. The reason to stay in Birmingham initially is the proximity of relatives, and lesser rents, However, plan to shift later to Oxford when my family is a bit settled. Please provide guidance on the following queries:

Queries

a. Would it be a problem to show my residence in Birmingham if I am studying in Oxford?
b. Can I do the tenancy contract directly with my cousin instead of going through an estate agent?
c. Can there be a problem with regards to the occupancy details for 5 people in a 2-bed house?
d. Can I say that it's a transit location in Birmingham and will be shifting to Oxford when we are a bit settled?
e. Any other aspect I need to be careful about?

Where are you reading that proof of housing is needed for a Student dependant visa? It is not.