I guess I like my eyes the best, because my friends admire itstheir color and shape.

You would use "their" in this case instead of "its" because your eyes are plural.

Actually, these are hereditary from my mother, so I have to appreciate herher to thank.

To say "I have to appreciate her" is not grammatically wrong but gives a different idea than what you wanted. In English, we say "I have her to thank" or if you got a new job you could say "My friend got me this job, so I have him to thank".

Actually, these are hereditary from my mother, so I have to appreciate herI inherited my mom's eyes, so I have her to thank.

I guess I like my eyes the best, because my friends admire itstheir color and shape.

AI actually, these are hereditary inherited them from my mother, so I have to appreciate ther. genetic gift!

I added in "genetic gift" which can be a playful phrase when people talk about things they've inherited looks and skill wise from family members.

I guess I like my eyes the best, because my friends admire itstheir color and shape.

eyes are plural, so you need to use their instead of its

Actually, these are hereditary from my mother, so I have to appreciate her.

This is not incorrect, but it sounds a bit awkward. A better way to say this would be "Actually, I inherited my eyes from my mother, so I have to thank her for them."