I bought some precooked whole shrimp. Do I need to peel and devein them before eating or is it possible to leave this step out? I intend to saute them in garlic butter.
Yes you need to devein them. The 'vein' is in fact no such thing; it is the intestine, and is thus filled with waste matter.
Yes, you need to peel them. Shrimp shells are indigestible, and serving shrimp (unless meant to be eaten with the fingers) with the shells on is, to my mind, indefensible. There is simply no good way to eat unpeeled shrimp with cutlery.
I would personally eat them cold, as I see no point in re-cooking something that has already been cooked. This will make the flesh tougher.
I disagree with Daniel, you can absolutely eat the "vein" in a shrimp. Whole un-peeled shrimp are called peel-and-eat and that's exactly what you can do. Basically, when you are first cooking the shrimp you get the make the shells on/shells off decision and if you go with shells off, you should de-vein, otherwise you just serve as is.
As for preparing already cooked shrimp, you can heat the butter then toss the shrimp in that off the heat. You won't get them hot, but you can knock the chill off while at the same time adding the flavors you want to the party.
I agree that already cooked shrimp is inferior to raw, but you can still make it taste amazing.
The fact that the intestine contains waste matter is a non-issue to your digestive tract, de-veining is mainly a presentation decision and not a health one.
You can leave both steps out if you wish, although personally I would always devein my shrimp before using. While consuming the 'vein' is harmless, I don't like the idea of eating it.
It is fairly easy to deshell the shrimp before or after cooking, so that is up to preference and cooking application may have a factor. If your shrimp are going to be fairly dry after cooking (which is not true in this case) then its easy to peel them after the fact. Because the shrimp are going to be cooked in a sauce it will be messier to peel after cooking; but if you don't want to touch raw shrimp/don't care then peel after. As Sarge said, cooking in the shell is more flavorful.