I have some minerals in Ward Co., but they have been held by production for a long time. Although I probably know about most of the minerals I own, from my experience it is not terribly uncommon for me to find out I own minerals somewhere only when I am contacted by someone wanting to lease them or buy them.
Do you know whether the outfit wanting to lease your acreage is an oil company or if it is a lease broker? If it is the latter, ask who they are leasing for. If they refuse to tell you, that is a big red flag.
Unless the party who will ultimately own your acreage is a well known company with a good reputation (not necessarily a very large major or independent), I would suggest that, if you do decide to lease you either ask for the bonus check from the landman upon signing, if in person. If it is done through the mail, you might ask that an instrument called a "sight draft" be sent with your lease after you reach a verbal agreement.
A sight draft is something you can cash a certain number of days after returning the executed lease, assuming everything was done right. This gives the oil company time to get the returned lease and see that it is properly executed. Not many companies that I know use sight drafts anymore, but you hear more than a few nightmarish stories these days about people who either have to wait months before they receive the lease bonus money they were promised or never receive it.
If you add the bonus amount per net mineral acre you have been offered to this thread, others who may have leased in your vicinity can possibly let you know if your offer is way too low or really good and everything in between.
It certainly varies as to the time offers to lease are good for. From my experience, 30 days is most common. I would not personally really consider 15 days a big red flag. However, I would strongly recommend that you do not rush into anything until you have done all your homework and are comfortable with the lessee and the terms of the lease. If they really want to lease you, they will normally extend the deadline. However, I cannot guarantee that they will.
In my opinion, the most likely reason that they made it 15 days was to cause exactly what has happened with some of your family members--create stress in hopes that you will rush in because you are afraid you might "be missing out on an opportunity".
Good luck to you!