Yes, this sentence can be translated as 'In the summer, he/she/it does not eat too much.'
Nope, that would be "nejedí" in Standard Czech.
Though, it's somewhat common to use "jí" for 3rd person plural as well, at least in Common Czech. Personally, I don't like it and would advise against using it. Adds unnecessary confusion and sounds extremely sloppy. O:)
"He" and "she" also are accepted, since the sentence does not indicate gender.
I would think that it would refer to an animal and then wouldn't the verb be zere?