How the installations of all 3 are different? If, for example, I'll go with RPM will it be easy later if needed to replace it with TWM or MS?
The RPM just bolts right on to the existing rod, and both TWM and MS replace the rod entirely. So, having the RPM on there doesn't make any difference. Just unbolt it and sell it.
Both TWM and MS require that you cut the stock shifter in order to remove it and install their replacements. This means no going back to stock unless you've got some welding equipment handy. With the RPM adapter you just remove the bracket. It takes all of about 5 minutes or less, literally.
One problem though with the RPM is that Mazda makes every shift rod different. Quite literally. They all have the bracket where the linkage connects (and where our adapter connects to extend this bracket) in a slightly different location. This means that the shifter actually feels different in every application and in rare cases (very rare) it doesn't fit at all. The good thing is that since it's a sort of "hack-job" it's very customizable. There are a lot of mods to the mod that people have done to make it just how they like it.
I understand RPM will keep the feel and height of stock shifter but just make throws shorter. By how much?
It's about 30%. Not a lot of difference between the three really.
Forgetting about height what are differencies in effort, smoothness, speed of engagement and overal feel between Stock/RPM vs TWM vs MS? Which one allows for shortest and fastest throws?
As I mentioned before it's difficult to compare the RPM to the others because every car with RPM is different. But, as a general rule, it will be the notchiest of the three with shifts requiring a bit of effort sometimes. From my understanding (I haven't tried TWM) both MS and TWM feel roughly similar. And TWM with it's shortened height has the technically shorter throws, but you're nitpicking when you start getting down to the small differences.
And last but not least do you guys think that CP-E + short shifter combo will noticeably change what I'm looking to improve - responsiveness in city driving (something akin to obstacle course)?
CP-E for sure. The short-shifters... Hard to say. I guess it could. One of the best things about the RPM is that it's so cheap. And you can resell it and be out like $10-20. That's nothing in the grand scheme of mods. So if you find it doesn't do what you want, you're not out much. If you find it does but you want a "real" short-shifter you can go MS or TWM.
Oh, and change to synthetic fluid (I recommend Redline MT-90) if you haven't already. That made at least as much of a difference as the short-shifter in my opinion.