What type of FTL space travel is most plausible in your opinion?
It's difficult to say. They all use "magic", by the definition of Arthur C. Clark as "sufficiently advanced science that is indistinguishable from magic". The wormhole-punching thing requires either the ability to fold the entire universe then create a negative-energy hole connecting two pices of the universe together; that's an awful lot of "it just is" hypothesizing. "Warp drives" require the ability to create an entire bubble mini-universe and the capacity to split it off from out universe and rejoin it again, on command.
I think "hyperspace" or "transdimensional travel" is your best bet. Mathematically, those compressed higher dimensions exist. How to use it is the biggest hurdle. I mean, we can;t even draw a circle on a piece of paper, turn it into a sphere, move the sphhere around the place in our three-d universe, then put the sphere back on the paper and turn it back into a circle again. That's what "hyperspace" is like, only in three dimensions rather than two.
Is there a lore explanation for why we cannot travel to other galaxies in Elite?
They're really far away,with no stars or anything else to use as a waypoint or stopover enroute. The FSD, and the older hyperdirve, both seem to have a limitation on how far you can jump before you hit some kind of "energy singularity": the amount of energy required for a jump approaches infinity as you get closer and closer to that maximum theoretical jump range. You can't just plot a jump destination 2 million LY away and press "GO".
Is it more difficult to travel to another galactic cluster?
Not quite sure what you mean there. Other galactic clusters are a heck of a lot further away still than the other galaxies that are in our own Local Group cluster. But impossible^2 is still impossible.
How does a ship that goes 1000 km/miles per second suddenly stop?
Magic space brakes.
The earlier FE2/FFE games had ships that could maintain acceleerations (and braking thrust) measured in dozens of G, for weeks on end. The lore explanbation back then for how the human spaceship pilots didn't turn themselves into space-jelly every time they fired their main engines was that they were not sitting in chairs, but embedded in a bath of acceleration-absorbing gel. The pilot's brains were either genetically modified (if you were Imperial) or cybernetically enhanced (if you were Federal) to withstand the constant high-G accelerations.
In ED, all that goes out the window as we are clearly sitting there in chairs, held in place by what appears to be nothing more than super-velcro and magnets. I can only assume that the genetic modifications and/or cybernetic enhancements have gotten much better in the past 50 years.
How does a planet or station stop an incoming projectile? Some aliens could shoot a projectile from afar, it gains speed until it hits a planet or station. Such an impact would have catastrophic consequences like a big asteroid.
It's not an issue that seems to come up in ED. Small-arms munitions such as those we use on our ships - the missiles, bullets and cannon shells - seem to have tiny built-in self-destruct mechanisms in place, to render them harmless once they fly a few km out of the main combat arena. This is presumably a safety measure, to prevent a decades-old missile from slamming into a space station millions of km from where it was launched.
The issue of using kinetic energy weapons (big flying rocks) as planet-sterilizing weapons of mass destruction has never seemed to have arisen. I know of no lore concerning any such attempts. Even WWIII, the mid-21st century horror that nearly destroyed Earth and humanity, never used such weapons. Nor did the desperate struggle between the Federation and the nascent Empire seem to have used such tactics. Not even the Thargoids at their most genocidal have used this. It is a curious omission. All I cna offer is that, after WWIII, mankind realised that using planet-killing weapons really weren't in anybody's interests.
Are projectile weapons better than lasers? Because lasers cost much energy.
If we're talking weapon theory, rather than their actual in-game implementation in ED:
Projectile weapons have the advantage, and the curse, of being "fire and forget" weapons. All the energy expenditure is utlilized at projectile launch, after which no further energy input is required. Low energy, but the disadvantage is that they're relatively easy to avoid. Under certain circumstances, you can even see the projectile coming towards you and react swiftly enough to actually dodge the bullets, Matrix-style. And if the shooter realises they're going to miss, it's too late - they can't alter the course of the bullet once it's fired.
Lasers require much more energy to cause damage, but the beam is speed-of-light fast; it can't be seen and dodged. The shooter, if they realise they are missing, can nudge their weapon a bit to get it back on target and resume damage infliction.
