If multiple effects modify your hand size, apply them in timestamp order. For example, if you put Twenty-Toed Toad onto the battlefield and then put Spellbook (an artifact that says you have no maximum hand size) onto the battlefield, you would have no maximum hand size. However, if those permanents entered in the opposite order, your maximum hand size would he twenty.

Your maximum hand size is only checked during the cleanup step of your turn. At other times, you may have more cards in hand than your maximum hand size.

Twenty-Toed Toad's last ability will trigger whenever it attacks, no matter how many counters are on it or cards you have in your hand at that time. The number of counters on it and the number of cards in your hand are only checked when that ability resolves.