If Hive of the Eye Tyrant enters the battlefield at the same time as one or more other lands, it doesn't take those lands into consideration when determining how many other lands you control.

If you turn Hive of the Eye Tyrant into a creature but haven't controlled it continuously since your most recent turn began, you won't be able to activate its mana ability or attack with it.

If you activate Hive of the Eye Tyrant's last ability multiple times, it gains multiple instances of the triggered ability that exiles cards. For example, if you activate it twice and attack, you will choose two target cards to exile (or the same card twice, if you want to).