Do civilian employers still have to pay me my salary while I am at annual training?

I don't think so, but I would recommend you contact your nearest Department of Labor and they should be able to answer that question. Because when I looked up the USERRA, I didn't see anything stating that salary employees are to be continually paid. I could be wrong, though. One caveat on something I read is that if you worked part of the week in your civilian job and then left, you have to be paid.

There never was a requirement to pay anybody anything. You must have been listening to urban myth. The Feds and some states like Texas pay up to 15 days of military leave, but that's an administrative choice (regulation), not law (USC). That's it. No other entity is required by law to pay you. It would fail in the courts as an unfunded mandate thing or improper taking of property. What some companies do is make up the delta in pay (time limit there too) if your MIL pay is less than regular pay. Others just call it unpaid leave and bitch about having to take you back.

It depends on your employer. If you work for a state, county, or municipal entity, then I believe Texas law provides that they must continue to pay you. Many private employers also provide paid military leave. Make sure that your employer knows that you are taking leave for military duty, not just vacation time. These folks can give you more specific guidance:
https://www.esgr.mil/About-ESGR/Contact/Local-State-Pages/Texas

There is no Rule in Texas for your Employer to pay you! They can choose to if they want. When I came into the Guard in 70, my Company paid the difference of what I was making compared to my Annual training. They didn't have to. At a different job they didn't pay me for being gone; but they did bank my PTO (40 hrs)and Vacation 3Weeks. They didn't have to either. I was gone plenty from Oct 2001 till Sept 2007. Wife loved it ! Pay was great from 2002 till retirement (22 1/2) in Dec 2007.

They can't require you to use vacation days but any days off beyond any military leave they may offer would be unpaid.

No. Read the book LT. I had majors work for me as a GS 13. You should to back to school

No, some companies will pay you, some won't. You can check with USERRA but pretty sure you are not entitled to pay.

No they do not have to pay you. I work for the VA and they give me 15 days of paid military leave a year (which I am thankful for!), but once that leave is used up I must use my vacation time if I want paid my VA salary. If I don’t have leave then I go into leave without pay status and just have to eat the loss. Yeah it sucks. Especially since I had to go to 4 weeks of training for a school and then will have over 3 weeks at another school this year, and I also have to take almost a week off for travel to and from quarterly drills with my home unit over 1000 miles from my home.

It depends where you work. In NY a private company does not have to pay you.
You should call the department of labor and ask them.

2LT (Join to see) the way my employer does it, sir, is that they continue to pay me. However, they will only pay the difference between what I am making from the military and what I would normally make annually if I were only getting paid by my employer.