On leased land

I have 2 questions: (1) A leased deed is registered in 2018 for 10 yrs of a vacant site for constructing a clinic on payment of annual lease amount, with a clause for extension of lease on mutual agreement. On my recent request (due to delay in building construction) the lessor agreed to extend the lease term from 10 to 20 yrs from 2018. Can we register a second lease deed NOW for the unexpired period of lease of this 20 yrs from 2018 (ie for 16 yrs from 2022 to 2038), without cancelling the first lease deed and entering into a fresh one for the total 20 yrs from 2018 (OR) can we register a second lease deed NOW in continuation of the first one for the extended 10 yrs, mentioning that the total lease period shall be upto 2038 reckoned from 2018. There are no significant changes in the T&C of the first lease deed. (2) Whether it is mandatory that the property tax on vacant land (set off), on building constructed by me as lessee should be paid on Lessor's name only. Quoting relevant Act/Rule/Court Judgmt is solicited' From MV Krishna, Chittoor