1. If it is not stated either way, no mineral rights are reserved or retained. In 1845, people didn't have the mindset to reserve minerals much. They were still riding horses. Spindletop, for example, was still 56 years off.
When you say his name is still on production for the property, I'm guessing you saw a well sign or something like that. They may just be referencing the original land grant. If there are any wells on the property, someone should be receiving royalty payments. It will be difficult if you haven't done it before, but you can go to the Nueces County Deed Records and see who has been leasing the land for oil & gas, or someone with research experience could probably tell you that fairly easily. As far as production, if you can figure out how to navigate the Texas Railroad Commission site, their maps would show you where wells are located, if any, dry holes etc...
2. No one here can really help with specific title questions, unless they researched it themselves. That typically takes time and costs money.
From what you have written however, it sounds like your family sold both surface and minerals in 1845.