2) Less research is a non sequitor, if one is going pure smaller, then there is no "less research" and if one is going for "more advanced" then once again, the research is going to be done regardless. Comparing different tech levels to one another is rather frivolous, especially in hindsight, either one wants/needs a tech or one doesn't, so there is no "research cost savings" ever.
If you use smaller gauss you need less turrets and the gun itself are cheaper to research so you need to research less number of turrets and the turret is less costly to research over the equivalent version. So you will save in research cost.
I will grant you that this is technically true, but it's also not that much for the benefit you get. I just ran the numbers, and in a fairly high-tech game (gauss ROF 5/range 5) I would spend less than 2000 RP to deliver a quad 100% gauss from scratch. Extra turrets will be under a thousand each. Oh, and you've spent 134,000 RP in basic research to get to those gauss guns. So the trade here is spending an extra couple thousand RP (maybe 3% of what you've spent on gauss so far in the game) in exchange for 20%+ fewer leakers (or, you know, 60%+ fewer leakers with good FC). Now, the best option I can see for that kind of 20% reduction in (effective) leakers is another level of missile jammer, which is, oh, 80,000 RP. Yeah, I think I'll spend the extra research.
One example ship I created with 4 100% quad turrets and one with 12 33% quad turrets used 20% (1200 vs 1500 supplies) less supplies and was 200t smaller, less crew and slightly cheaper to build. That is why it is not a straight answer to what is best.
Let's say that your FC has a 50% inherent to-hit, and you shoot 4 v 1 at 50% Ph with the basic ship. I get 6.25% leakers. Now, if I shoot 12v1 with the 33% ship, I get 11.22% leakers. You have to shoot something like 15v1 to get the same leaker rate (technically, the slightly-higher 6.49%). To put it another way, if you're bound by the total number of guns and want a constant leaker rate, you need 25% more ships. So the full-size gauss ship needs the same number of supplies, and is cheaper everywhere else. I'll take that one.
(Edited to fix basic math error in my last paragraph.)