Nightflier:
Each splitter will cost you 1/2 the signal strength or 3dB (no free lunch) but a band splitter if properly made will not cost 1/2 the signal (i.e all the FM will go to one output all the TV to another). They make 3, 4 and even 6 output splitters if you have a strong signal or cable that works fine. They even make amplified splitters, 'course those use a wall wart.

Yes you can "add" antenna signals but the weaker one will deplete the stronger in this case. Unless each antenna is a single frequency model. In worst case scenarios, I've seen installations with several single channel antennas facing different directions sumed with a splitter.

Whatever6750:
I have never seen a through wall/window coupler for FM you can make one but it will look silly. Paste one of those "T" shapped antennas on the outside of a window run the wires to the antenna on the roof. Paste another "T" shaped antenna on the inside of the window as close and aligned with the outside one as possible. The two antennas will couple the signal right through the glass.


Suppose a hill or cliff blocks the signal from the city? I have seeen people place a high gain antenna on the hill behind their house, with that antenna wired directly to a second antenna facing down the hill towards their house. Now a third antenna on the rooftop aimed at the second antenna on the hill will let the house "see" over the hill. Neat eh? (Lossy, yes, but workable)