to qualify the investment in case of builder flats, the crucial date is the date of allotment of the residential flat and the payment of installment is a follow up action

2)The date of acquisition of the said flat shall be the date on which the allotment letter is issued to the intended buyer.

3) in your case august 2015 would be regarded as date of acquisition of flat . Merely because the builder failed to hand over possession of the flat to the taxpayer within the specified period, the taxpayer cannot be denied the benefit of the said benevolent provision.

You can claim ownership or title to the property only after the sale deed is executed and registered on your name.

For calculating LTCG the date of registration may be taken into account though you have already paid the full consideration amount.

You should not have paid the entire amount in a haste anticipating immediate registration.

Well if the delay is inordinate then you may seek interest on the amount your have paid towards consideration

Without acquiring the property what prompted you to disclaim HRA, you should understand that you can initiate action not to claim HRA only after the property is registered on your name, until then the property do not belong to you though you have paid the full consideration amount

Can I claim loss on self occupied House property from the date of assignment agreement in place HRA exemption u.s 10(13A) of IT Act 1961?

You may not be eligible for this exemption may be because you have not got the property registered in your name and this deed of sale agreement will not confer title to the proeprty