OK, here we go....and hopefully not right off the runway and over a cliff....
1.) Texas International
As the placard on TI's bulkheads used to say, "Yes Sir, Texas International!"
3.) Northwest?
Northwest flew a lot of 720Bs between SEA and GEG, but never out of BFI. We're looking for a different airline here...
4.) Southern (note: I recently asked this question as well....)
Sorry about that - I must've been away when this question was asked. SO is of course correct!
8.) BAC One-Eleven?
That's the one!
11.) Northeast
Right on!
13.) Braniff International
That's right! Now what color was it? 
14.) Northwest and Western, both with the Lockheed L-188 "Electra" (BTW, the last time I flew out of Butte, it was on board a Delta B727-200 in F on a routing of BTM-BZN-SLC. And shortly after that, mainline jet service to BTM was apparently cancelled forever......)
To quote the late, great Ed McMahon: "You are correct, Sir! Ha, Ha, Har!!" I loved flying through little airports like BTM. Northwest, Western and Frontier brought propjet service most every major city in Montana. The Allison 501 was the official powerplant over the Big Skies of Montana.