Can you tell me if using the white food coloring mixed in alcohol will give me an opaque white paint that can be used on colored fondant?

Also, I have seen on cake shows the artist using a tape of some kind to make a straight line. Can you tell me what kind of tape is safe to use?

Painters tape is the tape you are probably thinking of.

I used it recently but had a few issues with it wanting to stick to my cake.

I think the opaque-ness is going to depend on how much liquid you add. I haven't worked much with white food coloring, only the white airbrush colors, which can be pretty solid colors.

I think for opaque you may need to mix it with piping gel.

Maybe worth playing with on some colored fondant to see which gives you the look you are going for.

Tutorial for tartan/plaid (might give you some ideas about painting straight lines):

http://www.cakescanada.com/HowTo/tartan_tutorial.pdf