(a) You should explain PPF account.
(b) One has to pay interest when he takes loan which is unlawful and haram. You must avoid the curse of interest if you feel no trouble living in a rented room and save money for a house.
(c) LIC involves interest and gambling and both are unlawful. According to Hadith, both bring loss at the long run.
(d) If money through mutual fund is invested in business and you share in the benefit and loss of your invested money as per the average, then you can invest your money in it. But, if the benefit is fixed to be received ultimately, then it is not allowed to partake in it.
(e) You should write details about NSC and submit the question again.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband