1. If their are producing wells, it's when they quit producing. Otherwise, the lease will state something like 3 yrs, that is from the date signed. Unless it has an extension, then they have to pay a bonus which is stated in the lease.
2. Whomever signed the lease agreed to a percentage of the royalty.
3. When a lease is sign, it can go to any company.
4. Lessee will collect taxes that are due to the government or state. Plus several other taxes. Oil companies can put liens on the mineral they have leased, kind of like owning a car, if it's paid for, you can mortgage it to get money.
5. You should be able to go to the county clerk office were the leases are and purchases copies of the lease or you can hire a land man to do it for you. Sounds like you may need to join the NARO in your state and get some education on owning minerals.