Welcome to Rega!
I'm sure others will give a more thorough reply but here's my take.
1. If you want to tweak the speed of your turntable the Rega might not be your best option. But, it should be pretty close, to spot on.
2. I've never heard a Rega cart so forgive me, but I'd buy an RP3 without a cart and buy something other than a Rega. I'm sure the Rega cart's are fine though.
3. hmm, I've never noticed, but my p3-24 is about a foot away from the right speaker on a components shelf. I've never had any feedback with it, You should be fine, but you can always experiment.
4. Other tables to look into? hmm, the new VPI traveler looks interesting or a VPI scout or even an RP6.
I think you'll really love the RP3, buy it with a 30 day money back and check it out. It has the same arm, plinth, motor as the RP6. Also make sure everything is spinning correctly with the Rega. Rega is very good about making things right if the subplatter for example has a wobble in it, stick with the table and you'll be rewarded. It's interesting because you can really tweak a Rega but you can't tweak the speed, azimuth or VTA (on the fly only with spacers) but somedays I'm happy that way, there's too much tweaking in audio that makes me lose my mind.
Also, be careful with all the tweaking, you can spend a fortune. The RP3 with the Groove Tracer Reference subplatter is all you need IMHO!
Rega P3-24 | Groovetracer Reference Sub-Platter | Rega Stock Belt | Shure M97XE w/ Jico Needle | Rega Brio-R | Pioneer SP-FS51-LR Speakers (Andrew Jones)