Can a faculty on a 12-month appointment apply for grants? I'm wondering if a 12-month appointed faculty (mainly teaching but also research duty, R1 university in the US) is allowed to pay him/herself from grants (especially NSF or NIH). I heard that they may buy the time with grant money, but I haven't heard if they can be paid extra. Also a rumor says agencies sometimes don't like to trade course loads.
Does anyone have experiences with these? Thanks.
This will entirely depend on the nature of the position, and "12 month position" isn't actually precise enough to answer it. There are several factors to consider:


There are 12-month faculty positions (including my own, and many positions at medical schools and other institutions) where not only can you bring in research funding, but you are expected to do so. The most extreme version of this is 12-month positions with 100% soft money. In my experience, this is actually the type of position the NIH is used to dealing with, in contrast to the NSF.
"I haven't heard if they can be paid extra" - this will again depend on the position. One institution I was considering a job at had incentives in place such that you could indeed pay yourself extra if you brought in grants (and one place actually automatically paid you more if you brought in more grants). My current institution only covers 75% of my salary, so covering the other 25% is technically "paying myself more", but it's capped.
Buying out coursework time is contingent on the department among other things.


Basically: Yes, but the nature of how falls under "It depends".