Not fast enough. Especially since you can make armors designed to withstand lasers longer. Carbon armor has a high vaporization energy and is great for that purpose.
Not as good as graphite, see the earlier remark about a meter of graphite armor at 5000 k (which is knife fight range.)
A sapce shotgun would be terribly ineffective. The spread of shrapnel would be too great at the distances invlolved. It wouldn't hit anything. A "smart" bullet would be a far better solution.
A 'space shotgun' isn't a shotgun at all. The objective is to deny an area of space by flooding it with shrapnel. It doesn't have to be fired all at once, shotgun-style; you just need to put a lot of crap into the target's flight path. You can use missiles to get a shrapnel warhead closer. Great way to get a kill, especially if you're scattering a ton of dust.
A smart bullet is just a missile. Already addressed. You can launch it from a coilgun if you like, though.
Oh no?
Followed by a laundry list from the website I linked earlier.
Those factors are all explanations for why lasers won't constantly hit. As I said time and again earlier, lasers can miss. Keeping a laser on a target, however, is not particularly difficult - it's one of the easier parts of the challenge today.
It's a hell of a lot easier than aiming a kinetic energy weapon, and at knife fight range the laser is a better bet. Every kind of weapon has its place. KEWs are the trickiest to make useful, though.
Please read what people post.