1. Yes the owner has to inform if the property is under lease.
2. Yes lease for rest of period has to be transferred in your name .
3. Sir since the lease is on agreed terms either you modify it with permission of pump owner of in case they donot agree since lease if for 30 years there shall be problem in sale of same portion.
4. Sir for that it need to be negotiated rent can be only increase and the owner shall only increase in terms of the lease deed.