Yes, tax liability will arise on capital gains arising out of difference between sale consideration and purchase consideration.
As far as rate is concerned, tax will be computed @ 20% plus surcharge (if any) on long term capital asset held for more than 24 months. While tax rate will be 30% plus surcharge (if any) if the asset is a short term capital asset.
if the property is acquired in the name of the partenrship firm, then the rights of the partners to such property would be governed by the terms of the partnership deed. As such, your partnership deed with your friend should spell out the respective shares of the partners in all assets of the firm etc.,
You can file a suit for seeking possession of the flat or in the alternative approach the authority under RERA seeking compensation for delay in handing over possesion of the flat and also for possesion of the same.
The open car parking would belong to the society/ organisation of apartment owners in common and they alone will be entitled to decide as to who gets to use such open car parking space.
Registration is required to be done within a period of 4 months from the date of execution of the Agreement. There is also a provision for further period of 4 months for registration subjet to payment of penalty.