Can’t see that your question got transferred to the Fayette County Texas section of the forum, but I think you should be able to find a lot of that information you are looking for on Texas Railroad Commission’s website.
You can pull up the map of that area from the link below (put Fayette in the Select County pull down menu at the upper left side of that page, click it to see the map, then move to the area of the county that you are interested in; Enlarge the map by scrolling to see the wells and permitted locations in the area you want to check then click them to see details on operator, when drilled or production)
http://gis.rrc.texas.gov/GISViewer/.
To track leasing activity try the deed record indexes on TexasFile.com or CourthouseDirect.com. You’ll need to set up a free account but then can search the deed index for Fayette County at no cost. There is a charge if you want to view or print documents.
If you know survey or abstract names or numbers in the area you are interest in you can do a property search for new oil leases in those areas. At CourthouseDirect.com you can also register to get a free weekly email with all the new leases recently recorded in your county, and it’s free to view the documents attached with that email. Most will just be lease memorandums, that don’t include all the terms of the lease, but they can help you follow the current activity in the county.