All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The question is not clear, but, in general, there are no Islamic prohibitions in what you mentioned except the interest resulting from the mortgage because it is forbidden to engage in interest-based contracts unless there is a compelling necessity to do so. And there is no necessity in owning a house for someone who can afford one by renting it, and the government pays the rent and will not stop it unless he owns a house.
Interest is extremely forbidden and leads to very serious consequences. Allaah says (what means): {O you who have believed, fear Allaah and give up what remains [due to you] of interest, if you should be believers. And if you do not, then be informed of a war [against you] from Allaah and His Messenger. But if you repent, you may have your principal - [thus] you do no wrong, nor are you wronged.} [Quran 2:278-279]
Also, the Prophet said, “Allaah has cursed the one who consumes interest, the one who gives it to others, the one who records it, and the one who witnesses it (its transaction).” The Prophet said, “All of them are equal in sin.” [Muslim]
If you entered into the contract, bought the house, and are obliged to pay the interests, then you may pay the mortgage from the government assistance while sincerely repenting and regretting what you did, and you should seek forgiveness and be determined not to do that again. For more benefit, please refer to fatwa 86527.
Allaah knows best.