What is the difference between AM and IP
$AM$ is defined to be $AM[2]$, i.e. languages with 2-rounds Arthur-Merlin protocol, which is equal to $AM[k]$ for any constant $k$.

Two extra rounds are required to overcome the fact that the coins are public, i.e.

$IP[k]\subseteq AM[k+2]$ for any $k$ , constant or not, as stated in complexity zoo.

This means that $IP[poly]=AM[poly]=PSPACE$ (which answers your second question).

If $IP$ can be limited to a constant number of rounds (rather than polynomial), then we would have $PSPACE\subseteq IP[k]\subseteq \Pi^p_2$, and the hierarchy collapses to the second level, since $PH\subseteq PSPACE$.