"Batısında" is used in possessive form. For example you say "Evin batısında" which means "in the west of the house". While "Batıda" is in its normal form which means "in the west". In this example, we have to write the word "batıda" in its normal form. Hope you got it!
"Limonları" would make it "turtles eat the lemons" -- that is, they'd have to be particular lemons. If we're just talking about lemons in general, the object doesn't get the plural or accusative endings.
Good question -- when using the Aorist verb form (which you use for habitual actions like this one, e.g. "yer", "okur" etc.), any direct objects are understood to be plural (unless it has "bir" in front of it). :)