Matching your watch strap to belt/shoes is fine, but not necessary. I do it as often as not. It's more important that the watch itself compliments the overall outfit.
Probably not. But I'd wear a mid to dark brown leather band with tan shoes without a second thought. They wouldn't match, and that would be just fine by me.You'd wear a black leather band watch with a tan leather belt and shoes?
I can see, for example, a black leather band with a dark chocolate pair of shoes, or the other way around.