Amen and amen. The whole conception of the series borders on heresy.
At least DS9 didn’t have any stupid beards!
To paraphrase Lucy Lawless (on the Simpsons, of course) “Whenever you see something that doesn’t make sense, a wizard is responsible.” “Or Q. Whoever.” 
Humor…it is a difficult concept.
IIRC, in the TNG episode Brothers, at one point Picard asks about separating the saucer section. The idea being that within two minutes, the saucer section would drop out of warp. Of course, Data had locked out all command functions so it couldn’t be done.
I just watched “The Apple” again (shudder) and I don’t quite remember that line - though it might be one that was cut.
Another hint was in “Tomorrow is Yesterday” the one where they go back, unintentionally to 1969. After they go through turbulence, Spock says something about “if Mr. Scott is still with us,” - then the power comes on, and he says, “Mr. Scott is still with us.” I take this as a reference to the possible separation during the stress.
I swear I’ve read something where this is made explicit, but I can’t find it in either the first ToS Technical Manual or the ST Writer’s Guide.
I take it as a reference to the possible Scotty being dead.
DS9 (also called "the best of the Star Trek franchises) debuted January 4, 1993. Babylon 5 debuted January 26, 1994, being based on a TV movie that aired February 22, 1993. So therefore, it looks like Babylon 5 is, if anything, a TBOTSTF rip-off.
Nah, the pilot script for B5 was floated around Hollywood for years before it actually debuted. It’s commonly believed among B5 fans that while it was at Paramount, it was handed over to the Star Trek writers with instructions to “come up with something like that”. (Working on memories of the conspiracy theory here – could be wrong about the details, but I’m sure that B5 was earlier in concept, and definitely not a rip off.)
I love to fanwank. So here’s my explanation:
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Warp field sustainers keep the saucer and photon torps going for about 2 minutes.
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The saucer section could rendezvous with another starship for link / tow the rest of the way. (like a tractor trailer)
That would be the Hood then. It was the only other starship in the area, and was transporting Dr. McCoy somewhere important.