"There is an egg."
Translation:Υπάρχει ένα αυγό.
Well, I'd say the cases of υπάρχει being interchangeable with έχει are few and way too specific. Plus, I think you'd use it a bit more often for non countable nouns or with plural, like
exp. There is milk in the fridge - Υπάρχει/Έχει γάλα στο ψυγείο.
exp. There are apples in the bowl - Υπάρχουν/Έχει μήλα στο μπολ.
It's a relatively common thing to hear in spoken Greek, I don't think it should be accepted though. It's a bit too slangy, and it might cause some confusion. ^.^
Both of them are used for "one" or "a".
ένας is for masculine nouns
μία is used for feminine nouns
ένα is used for neuter nouns
All nouns in Greek belong to one of those three genders. αυγό is neuter (as are (essentially?) all nouns which end in -ο in their dictionary form) and so ένα is correct here.
ένας ανανάς και μία φράουλα και ένα αυγό "a pineapple and a strawberry and an egg"