As Clint mentioned, that is a great area to own minerals. To answer your question about section sizes, a section is typically 640 acres, one square mile, but in certain instances they can be much smaller or larger.
The section you are inquiring about, Section 28, Block 55, T1S, is described on the Texas General Land Office website as being 640 acres.
It is definitely a good idea to find out what exactly it is your wife inherited, rather than relying on what the person that wants to buy the interest is stating she owns. It sounds like she may only own a royalty interest (only receives revenue when production from the land occurs) but it is possible she owns a mineral interest, in which case she could lease the minerals, perhaps for more money than the unsolicited purchase offer.
The best way to find out what she owns is to have title examination performed by a landman. By the sound of things, there could be other properties in the county that she owns as well.
Based on where this property is located, I would be hesitant to sell the interest, whether it be mineral or royalty. Or, at the very least, hesitant to sell all of it. If the decision is made to go ahead and sell, make sure that the deed does not have "countywide conveyance" language in it. In other words, make sure she isn't selling everything she may own in Loving County.
You might consider reaching out to one of the forum sponsors to see if they can provide information about what prices they're seeing in that area, as well as if they have any existing title for that section.
Best of luck!