Good Morning, Gang!
And, welcome back,
JL! Here's hoping you and Lady K had a fabulous and rejuvenating time frolicking in the waters off Key West. I'll be down at Key Largo a week from today, so let's hope the weather is every bit as nice for me as it was for you. Here in the Great White North the whiteness continues apace with an early April storm that dumped 16" of snow in the hills around Fairbanks and almost twice that down in the Park. A check of the forecast calls for five days of temps varying from -10 to +15°F each day, so we won't see any melting for awhile. Funny how just two months ago temperatures such as these would have been considered a warming trend. Now the forecast sez "very cold".
Meanwhile, back on the home front, let's start with:
29. (1987) It used to be that if you wanted to fly from Palm Springs to Las Vegas, Western Airlines was quite literally the only way to fly. These days (1987) there are three airlines offering daily nonstop jet flights on the PSP-LAS route. Identify them if you can… Feel free to additionally identify the jet associated with each airline’s flight.
These are all major carriers operating mainline equipment
Not PS/US, CO/FL, or Royal West; not a 737-200 or a 146
Not TW, HP, MC; however, one of the airlines we want did operate an MD80
Per jrl767: Given AA was the M80 operator and we have explicitly eliminated BN, CO, PS, and TW ... we’re left with AS, DL, EA, UA, and WA. As I mentioned in my initial guess, nobody ever said WA *wasn't* one of the three, so I’ll offer them and UA
Western had been absorbed into Delta by the time the schedules I employed to reference this question were published. United is however correct! Quite a surprise to me as this was not traditional United territory.
That said, all of Alaska's service into PSP came from up the west coast. I don't believe Eastern ever served PSP. It's flights out of LAS tagged on to RNO. That leaves Delta operating over a traditional WA route dating back to WA's early days, I should imagine. Here are the offerings:
American AA 528 Palm Springs (PSP) 843a-925a Las Vegas (LAS) MD80 Daily
United UA 374 Palm Springs (PSP) 1035a-1117a Las Vegas (LAS) 727-200 Daily
Delta DL 1536 Palm Springs (PSP) 106p-147p Las Vegas (LAS) 727-200 Daily
5. (1966) How exciting! You and your wife will be making your first trip to los Estados Unidos to visit with your son, his new wife and your soon to be born grandchild. It’s been years since you last got on an airplane and your son says it’ll be a big one this time – at least compared to the DC-3 you flew on last time. First, you’re booked on a direct one-stop flight from Cali to Miami where you’ll connect to a smaller plane for the nonstop flight up to Orlando. Both aircraft – though different from one another - are manufactured by the same company. Identify both airlines, the route including the enroute stop and of course both aircraft types.
Per Herb687: BOG was already eliminated in one of my guesses. CTG and EOH/MDE now eliminated too leaves only BAQ as a logical stop for the Avianca Connie. Must have been Barranquilla?
What's with the question mark? I ask the questions around here! 
That said, I'll put on my Alex Trebec mask and say Barranquilla is correct! It is Colombia's main port and was once the largest city in Colombia. Here's the schedule:
Avianca AV 666 Cali (CLO) 1000a-1105a Barranquilla (BAQ) 1150a-310p Miami (MIA) Lockheed Super Constellation Tu Fr
National NA 224 Miami (MIA) 500p-548p Orlando (MCO) Lockheed Electra Daily
BONUS: The Tupolev Tu-154 was also operated in scheduled passenger service into two U.S. cities located on the east coast by a foreign air carrier. Anyone care to guess the airline?
Good call, JL! I remember this one. I believe we're looking at Guyana Airways which flew from its base at Georgetown into Miami. What I'm not sure of is whether it stopped at Port of Spain along the way. As for the other east coast airport, the only one that makes sense to me would be New York (JFK)
More questions coming later this afternoon