Luftwaffe 98K- what did they have?

I am looking for my first WWII 98K and I am interested in getting one which was used by the Luftwaffe. I am new to the 98K, and will look at threads on here to learn, but here are my burning questions.
1. Are there particular makers of 98K that were used by the Luftwaffe? As in, if I want a Luftwaffe rifle, are there particular makers to look for?
2. I am aware of the Luftamt stamp- I understand there are numbers associated with the stamp which tell something about a location, but what does the Luftamt mean?
3. Any tips or "tells" to look for to quickly identify a Luftwaffe rifle?

Welcome to the forum, I would recommend looking at the picture reference thread but Luftwaffe contract rifles are scattered throughout most manufacturers up through 1941. Mauser Oberndorf was the largest manufacturer for K98ks in terms of pure volume and would be the most common to find for a Luftwaffe contract. I'm unsure if there were entire known suffix blocks dedicated solely to Luftwaffe production (hopefully someone can chime in on that) but there are at least 4 different manufacturers for Luftwaffe accepted rifles in the reference thread alone. The main tell is the acceptance stamp (Eagle/L) on the right side of the stock for K98ks (pic related). The Luftzeugamt stamp you are referring are Luftwaffe depots, on which there is an excellent research thread detailing their locations and work throughout the war that you can find stickied in this sub forum which includes reworked rifles for the Luftwaffe and depot built rifles as well.

If you want something fun all of the G29(ö) G12/34 whatever you want to call it were used by the Luftwaffe. But yes Eagle/L stocks were Luftwaffe just make sure the stock matches. There are also entire Luftwaffe depot built rifles with special marks on the receiver.