Adjectives and Adverbs – ‘I Did Well’ vs. ‘I Did Good’

As kiamlaluno tells you, it is non-Standard to use good where an adverb is called for.

However, there's nothing wrong with using it with feel. Feel is ordinarily used as what grammarians call a copula: its complement is a quality attributed to the subject, and is therefore an adjective, not an adverb:

I feel pretty! Oh, so pretty! I feel pretty and witty and bright!
I feel really, really stupid.
I'm feeling pretty bad today.

And (again as kiamlaluno tells you) “I feel well” means you don't feel sick, but healthy.

If you use feel with an adverb you are probably employing it not as a copula but as verb of physical action. “I feel badly” means your tactile sense is impaired.

In your sentences, either an adjective or a verb is being modified.

I can't play football _________ enough... (verb)

This house isn't protected _________ enough... (adjective)

I'm doing _________ / I'm doing _________ in this game ... (verb)

These words must be modified using an adverb. Out of your two options, there is only one adverb: well.

I can't play football well enough to be on your team.

This house isn't protected well enough.

I'm doing well.

I'm doing well in this game.

Quick note: for the last two sentences it appears as if you can take well away from the sentence -- you cannot. Do well is an expression. You cannot say "I do in this game", nor can you say "I'm doing." You can, however, say "I do." when you get married.