How many fighter pilots are active in the U.S. military at this time,
and how many new fighter pilots are trained each year?

According to a research conducted by the Rand research institute
(Taylor et al., 2002), there are 4381 fighter pilots in the US
inventory (ibid. p. 34).

According to Taylor et. al. (ibid: p. 89), each year, 330 new fighter
pilots are "produced" each year, out of 1100 who begin the process
(ibid.: 35).

William W. Taylor, James H. Bigelow, S. Craig Moore, Leslie Wickman,
Brent Thomas and Richard Marken 2002. _Absorbing Air Force Fighter
Pilots: Parameters, Problems, and Policy Options_  (Rand Project
Airforce)

Further Sources
===============
Google Search terms:
://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&imgsz=small&q=%22fighter+pilots%22+number+active

Air Force FAQ http://www.af.mil/lib/faqs.shtml 

I hope that answered your question. Please contact me if you need any
clarification on this information.

It took a while and I had to raise the ante, but the answer was right on. Thanks.