Long Term Capital Gains after purchase of property - Section 54F

Yes, you can claim.

There’s no additional form, just mention in the relevant part of ITR about the exemption claimed u/s 54F after adding the capital gain income in the capital gain schedule.

To avail exemption on capital gain, you need to buy a residential property within 1 or 2 yrs but construction of the property you will have  3yrs time. However, you have sufficient residential assets. You can go to buy bonds upto Rs.50,00,000 is a limit and time duration is 6 months. You can avail capital gain exemption u/s 54. 

As you mentioned RSU income received Rs.15 lakhs for next financial year. It will not be accounted into current financial year. 

So, you have capital gain income only for Rs.10 lakhs. As you mentioned, you recently purchase whether it was purchased by home loan not. You can avail Pre-Interest and principle and emi interest.