My initial question speaks for itself. The scenario is that I would like to be able to do some foley work outside, such as things like walking through brush or shooting a gun, possibly. If a shotgun microphone would pick up sounds like the birds chirping, is there a way to a) Remove the sounds of the birds chirping or b) any good way to record sounds indoors? (Mind you, most of the rooms have an echo. However, I could repurpose an old treehouse into a Foley studio, and put up sound absorbers if necessary).
Would a shotgun microphone pick up bird sounds?
Yes, depending on how quiet it is otherwise and how close you are to the subjects (birds). Nature recordists more typically use parabolic dish reflectors for long-distance pickup of medium to high frequency sounds (i.e. bird-calls). Remember that whatever you use must have GOOD wind protection. At least a substantial foam gag (that puts at least 2in/50cm of foam around the mic) PLUS a "dead cat" furry cover to reduce wind noise. Going out into the wild without wind protection is putting your mics at significant risk of damage.
Is there a way to remove bird sounds?
Maybe. It depends on many factors, and it will almost certainly be tedious, fiddly, and likely not as rewarding as the effort you put into it.
Is a shotgun good for indoor recording?
Typically NO. A shotgun mic depends on the angle of incidence of the sound hitting the barrel. If there are nearby reflections (ceiling, walls, floor, table, etc.) then it completely destroys the operation of the shotgun and yields results that are WORSE than a more "normal" microphone.
This also applies outdoors if there are nearby reflections. It also means that in a large room without nearby reflections, a shotgun will work fine. The qualifying situation is nearby reflections (or not). It is not a simple matter of "indoor vs. outdoor".
What can I do about rooms with echo?
Yes, you can apply absorbing materials to the walls, floor, ceiling, etc. This could be as simple as propping up old mattresses against the walls, etc. Or as far as buying fancy foam shapes specially marketed for the purpose, etc.
It is easier to mitigate internal reflections (echo, reverberation) than it is to actually BLOCK external noise from coming into the room.