Doesn't this tense in Turkish imply some sort of conditional meaning. The translation in English doesn't feel totally right. It seems to me that the best translation for this sentence is; "I would eat an egg."
It depends on the context. The plural is yumurtalar in many situations. However, if the subject is a non-specific direct object, it will be just yumurta. Here you must say an egg because of bir. :) Let me know if I answered your question. I can go into more detail!
That simply would be "I took/bought an egg." It has a different meaning in Turkish :)
"I am eating" is the present continuous tense "yiyorum." This is in the simple present tense :)