If I add Black food coloring to Strawberry(pink) frosting will it make the strawberry frosting taste different?

Do it. A drop or two of flavorless liquid isn't going to dilute the flavor of a whole cup or two of strawberry frosting.

Been there, done it, it's fine. No clue why you're getting answers saying the taste will be "off" or "diluted" - simply not true.

no

Food coloring should be tasteless

Food coloring is basically tasteless, so there shouldn't be any alteration of flavors there.

Don't think so.

Most black food coloring won't color that frosting a true black and it will be a noxious gray if anything.

Start with chocolat frosting and color that black..you won't have to add as much.

Too much of any food coloring can cause the frosting to taste bitter in some cases.

it shouldn't, just make sure to get a good quality one since black is so opaque

No, it changes the colour of the food, not the taste. Hence them calling it 'food colouring'.

no, it may be just a bit off but it should be fine, I like the idea of the batman logo, I wonder if I can do that to lemon frosting and use it on a lemon pie in place of any meringue? <sigh> I know I never will but ooo wouldn't a bake sale love that!

Of course it would dilute it - adding anything would dilute the flavour.