First off, to answer your questions:
1. Yes, you can just lop off the stock to turn it into one, which is legal in the US without a special permit, unlike if doing the same to a rifle, as long as the overall length is 26", as mentioned. Or you can easily buy aftermarket pistol grips for common brands like remington, mossberg, & winchester.
2. Above doesn't matter whether it's semi-auto or pump.
Now, to go beyond answering your question.
3. As mentioned, doing so makes the shotgun less useful for most purposes, including home defense.
4. If you're gonna do it (and thus fire with no shoulder stock), I would definitely advise not doing it to anything over a 20 ga, as the recoil would become brutal. And I wouldn't shoot 3" 20 ga shells, only 2.75".
5. Of course, as mentioned, keep the bbl length 18.1" or longer.
6. If you do just lop off the stock, and form a pistol grip of sorts from the remaining wood via dremel, etc. - 2 issues: (a) it won't be as vertical as an aftermarket stock, which will make it harder to control under recoil, and (b) you've just lowered the market value of your sporting shotgun, until such time as you buy a matching replacement full wood stock, so therefore cheaper in the long run to pick up a crappy or not-so-crappy used shotgun at a gunshow or whathaveyou, with or without an existing stock, or with plastic furniture.