Tere is and there are mean that something exists or happens, while the verb have (has) indicates possession. Sometimes they're interchangeable (like your examples 1 and 2), noticing that the verb have always needs a subject.
In you second example, sentence b makes no sense, because A man has two legs, he was born with them, no one placed the legs there.
And in your last example, sentence A is correct. The sentence B, though grammatical, sounds odd. Perhaps you could say 'I have four eggs on my plate'.
Retired English Teacher