It's actually never the case in TOS that the ship would orbit belly down; it only happens once in ST3. The preferred TOS orientation is portside down, offering equal planetary views for the top and bottom sensor domes, with one or two occasions of starboard down and one case of bow down. Similarly, a bridge would be in equal jeopardy atop or below the saucer. (The issue is sometimes confused by the tendency of the main viewer to show the planet at the bottom, but such views are also often combined with exterior views confirming the portside-down orientation.)
Still, there's something odd about the placement of the three supposed sensor domes. The small one atop the shuttlebay would appear to complement the one atop the saucer, but is unnecessary as the saucertop bubble has no blind spots of note. In contrast, the saucer bottom dome would definitely benefit from a repeater at the bottom of the secondary hull, but has none.
One might almost think the domes are dedicated weapons-targeting systems, the top and bottom ones being associated with main phasers and the shuttlebay one with the twin phasers seen there in "In a Mirror, Darkly" and on the refit vessel. Scientific sensors might be viewing through the "windows" on the sides of the neck, oddly placed (and curiously numerous) for portholes...
As for the placement of torpedo launchers, it seems self-evident: you don't really want
to have dedicated antimatter pods on Deck 11 where they can be pummeled by Klingons ("Errand of Mercy") merely to keep your antimatter torpedoes supplied with explosive material. You are better off spending your resources protecting a single antimatter citadel, a combined main powerplant and main supply of torpedo warhead contents. The weapons themselves do not particularly suffer from any placement over another, as they are extremely maneuverable and guided, and apparently can be fired "over the shoulder" ("The Changeling") even when a dedicated aft tube might exist.
Shuttles seem poor alternatives to transporters in keeping the landing party properly supplied. A shuttle can only carry a limited amount of gear; a transporter can provide the landing party with an unlimited amount. A team ending in a tight spot is screwed with or without a shuttle, but only if it cannot be extracted; a transporter can do that much faster than a shuttle. Also, the transporter is invulnerable in transit, while shuttles can be shot down or lost to storms or even roc-caliber birdstrikes.
If the landing party really needs the services of the shuttle, the sensible thing might be to strip the craft of its superfluous engines and simply beam it down!
there are two different ways of...
Naturally there would be. Otherwise what would be left for Kirk to do? He has to be able to make a command decision between existing options.