Can landlord enforce 7 yrold lease with no end date plus raise rent when lease shows different

A raising of rent must be agreed upon.

Typically only lawyers are permitted to negotiate.

In general, in New York, the additions/changes would need to be executed by both parties.

Landlord did not give any notice prior to entry

In general, in New York, a landlord is not permitted to enter, except if there is an emergency that must be addressed.

Can unpaid rent be withheld from a security deposit for unpaid last months rent?

In general, in New York, one is permitted to apply security to unpaid rent.