Ben bir yumurta yerim.

Ben bir yumurta yiyorum.

Ben her gün bir yumurta yerim.

Ben yumurta yerim.

I wanted to know if the first sentence is gramatically incorrect???

Are sentences 2, 3, 4 gramatically correct?

All correct.

Ben bir yumurta yerim: I will/would eat an egg.

Ben bir yumurta yiyorum: I am eating an egg. [The natural expression would be Yumurta yiyorum.]

Ben her gün bir yumurta yerim(yiyorum): I eat an egg every day.

Ben yumurta yerim: Again, I will/would eat (an) egg(s) or I eat eggs in general. I like them.

OK, thanks! I just wondered in because in English ´I eat an egg´ would not be correct. Unless it was an answer to a question like - what do you eat every morning?

It is nearly the same in Turkish, "ben bir yumurta yerim" is absurd (yet grammatically correct) unless it is an answer to a question..

Q- Her sabah ne yersin? -- what do you eat every morning?

A- (Ben) bir yumurta yerim -- I eat an egg

or

(at a breakfast table)

Q- Kaç yumurta yersin?

A- (Ben) bir yumurta yerim.

Please note that, in Turkish, aorist tense (which referred to an ongoing or repeated situation) is (as in the 2nd example) also used in place of the future tense.

Well "ben bir yumarta yerim" would be used in a situation like;

Say you go for a breakfast to your friends house and he asks you, what would you like to eat, egg, cheese, olive, honey etc..

You can answer

Bir yumurta bir dilim de peynir yerim.

But to answer the question, what do you eat every morning, the answer "ben bir yumurta yerim" is not natural. You can just say "yumurta yerim".