بسم الله الرحمن الرحيم
(1) As per the elder Muftis, income tax is a non-wajib and unjust taxation. Hence you may pay your income tax from interest amount received from the government, it is lawful.
(2) In taking home loan from bank you would deal in interest which is severely unlawful, haram in Shariah as well as cause of curse. It is not allowed except in the state of exigent compulsion. And here the condition of exigent compulsion is not found; hence you would not be allowed to take home loan from the bank. You should lessen your expenses and save some amount and buy any suitable residential house later on.
Allah knows Best!
Darul Uloom Deoband