Being a Tele lover myself, I'll take a shot at some o' these:
1) The hotter pickups have a more "driven" (i.e. dirty) sound. Personally, I prefer vintage pickups - you can add dirt to clean, but you can't add clean to dirt.
2) The Baja Tele has a very fat neck, but it's kind of a 'V' shape. Some like it, some hate it. The fattest neck is generally considered to be the one that comes on vintage "Nocasters" - but those are very spendy guitars! Another option is to order an aftermarket "fat" neck from a place like Warmoth, Allparts, USA Custom Guitars, etc. Warmoth has a "fat" neck that I really like (it's what I have on my 'Partscaster'), and the Allparts TMN-F neck is highly regarded by many who like fatter necks on their guitars. If you buy them pre-finished, they'll almost always bolt right on to your Tele with no mods needed - just remove and replace 4 neck screws. You can also order them with a wider nut, which addresses your issue at the end of your post. The one on my Partscaster has a 1 3/4" nut width.
3) Sometimes what makes them sticky in the shop is having fifteen million people with gooey hands playing the guitars!
Seriously though - nitro finish necks can sometimes feel sticky, but they'll usually "smooth out" after you play them a bit. If not, a light rubbing with some ultra-fine steel wool will help. Some of the poly necks with gloss finish feel that way too - I prefer the "satin" poly finish just for that reason....less "stickiness".
As far as the maple vs. rosewood thing - I find that to be corksniffery. Tone freaks who can supposedly tell such differences say that maple sounds brighter than rosewood, but IMO the differences are very subtle at best unless you have highly trained and extremely sensitive ears. I'm apparently not that gifted, so the biggest difference to me is looks.
4) One has six saddles, one has three.
Seriously though....besides looking more "vintage", some say that the 3-saddle bridge offers more "twang" and more sustain. I've got a few Teles - a couple with 3-saddle and a couple with 6-saddle. Sometimes I think I can hear a difference, sometimes not. The only one that it seems I can consistently notice a difference on is my 'Partscaster', which has an aluminum saddle for the E/A strings and brass saddles for the D/G and B/E. That one seems to have more twang and resonance, but it's so subtle that you don't really notice it unless you play it side by side with a six saddle Tele - and even then, the difference isn't earth-shaking. This is another area which I feel goes into corksniffery.
The other difference is that the six-saddle bridges make intonation easier because of the individual adjustments.....that's why some people who use 3-saddle bridges go to "compensated" saddles.
5) Ahhhhh - this goes into the dreaded "tone woods" debate. This topic is hotly debated amongst tone freaks, and once again I'll call corksniffery. IMO, the biggest difference is looks - pure and simple. I doubt that very many people could tell the difference in tone between different woods if you blindfolded them and had them listen to each guitar.
One of the guys on the Telecaster board did an interesting experiment a while back. He posted a sound clip and asked people to guess what kind of wood he had used in building the guitar. Guesses were all over the board, with some offering most excellent explanations why they thought it was such-and-such wood. Turns out he built the thing out of solid MDF ("particle board"), using a modern six-saddle bridge and a "blade" pickup.....about as non-vintage as you could possibly get, yet it still "twanged".
6) Personally, I LOVE the vintage Kluson-style tuners. Much easier and cleaner than tying "knots" in your strings when you wind them, with no sharp points to stick you. I have them on two of my guitars and will probably eventually swap my other Teles out for them also.
As for having one that sounds like Brad Paisley or Lee Kernighan - the biggest factor in their sound is how they play! That goes back to the "tone is in the fingers" thing.....Brad Paisley would sound like Brad Paisley whether he was playing his Crook Custom G-Bender Tele through a Dr. Z amp, or a Squier Affinity through a solid-state Crate. Sure, the gear helps - and Brad is a serious gear-monger and "tone freak" - but the bottom line is that no particular model of Tele is going to make any of us sound just like him. He plays several different Teles, all with different pickups, through different amps (most notably an old AC-30, a Dr. Z "Z-Wreck" and Stang Ray, and a Bruno UG30), but he always sounds like Brad no matter which one he's playing.