"What colors look good on me?"
You should think of "很" as modifying "好看" here, not just "好".
While it's common to use "很" to make a sentence sound less abrupt, and it doesn't necessarily add much if any emphasis, this principle is less applicable where "很" is modifying a two-syllable adjective or adverb.
In this sort of question, to my ear, adding "很" sounds a little strange, and somewhat presumptuous: "What colors look very good on me?"
1） Can I say 什么颜色的衣服我穿好看？
2)Is there any difference between the given answer 我穿什么颜色的衣服好看? and 我（穿）什么颜色的衣服穿得好看？
I want to put a "得" in your first sentence before "好看" to "correct" it, but I'd like to hear from a native speaker as to whether either version is actually correct.
Your suggestion doesn't seem wrong to me and seems to have the same meaning, but again I'd like to hear from a native speaker.