You can say "a coke" because "a" means one and "coke" is singular. You can't say "a noodles" because "a" means one and "noodles" is more than one. This is bad grammar. You don't order a noodle (singular). You can "order noodles" but how much is this, one bowl, two bowls, a plate, a quart in a take-out carton? Just order a bowl of noodles. It is simple, clear, and correct.

If you're in an exam, stick the BOWL back in! If you're in a hurry in a restaurant, it'll do just fine, and everybody will understand you.

This is correct.

'I'd like the bowl of beed noodles please' would be correct. You don't want to use 'a' in this context, because the indefinite article 'a' doesn't apply to the plural. 'I'd like the small beef noodles please' is also correct. There's lots of ways you can say this, but if you're wanting to speak like a Brit you'd probably just say 'I'd like the small beef noodles please' if you're pointing to it on a menu.

It's colloquial, and not strictly correct; but people can and would say that.