Mostly I alwaysI usually eating eggs every day.

The words "always" and "every day" each mean doing something at a rate of 100% - you don't need to use both. "I usually..." as above sounds nicer than the other potential alternative "I mostly eat eggs every day."

Not because I like ithem, but because my family member buy it every time it emptykeeps them stocked.

Eggs, as a food, are referred to in the plural sense (them).
Keeping a persistent supply of something (it could be in your home or a shop owner) = keeping a stock of the item.

I cooked them with tomatoes, and green onions.

I also tried somey other recipes.

The above is to mean you have (in the past) and you continue to (in the present) try recipes with eggs. But if you want to only speak about the past: I've also tried other recipes.

Mostly I alwaysI often eating eggs every day.

You can change “every day” with “daily”

Not because I like it, but because my family member buy itbuys eggs every time it empty.runs out.

I cooked it with tomatoes, and green onion.

When describing two nouns, don’t forget to use “and”