I don't have a grill or a grill pan ... can I cook these in the oven? Are there changes I should make to account for the cooking method?

A grill pan is just a skillet with ridges. I'd do the kebabs in a regular, large skillet on top the stove. You want to be sure to brown all the sides. I haven't made this recipe, but I've done kebabs stove-top w/o a grill pan...

I don't think so, except that towards the end, you'd want to broil them.
I think that these would be good in a skillet as well. I would just sear them on all sides.
This sauce is good enough that you could put it on anything. As long as the chicken is fully cooked, just dip it!