You can put the extra card in your active area to keep track of the bear's attack and move values if you want (consider it a lost card that cannot be recovered), but it should be pretty easy to remember after a game or two.

Command actions allow only the bear to perform the abilities on them - not the Beast Tyrant or any other summon.

Note that unless a card specifically says it only affects summoned allies you own, it can affect any summoned ally, including those of other players.

No. However, it is still considered a summoned figure.

No

Like any other summon, the bear will always be available to summon again in the next scenario. Permanent death would only apply if the Beast Tyrant himself ran out of hit points.

The shield for the bottom ability is NOT an aura. The target of the shield must be chosen at the end of the Move. The shield remains with that ally for the remainder of the round even if they move away.

This summon has no attack action or a base attack value. It has no move action or base move value. It cannot be commanded to attack or move with an "Attack +X" or "Move +X" action, but it can be commanded to attack with an "Attack X" action (e.g. the Mindthief's "Possession") or to move with a "Move X" action. It can also be pushed or pulled as normal.

This summon has no move action or base move value. It cannot be commanded to move with a "Move +X" action, but it can be commanded to move with a "Move X" action. It can also be pushed or pulled as normal.

This summon has no attack action or a base attack value. It has no move action or base move value. It cannot be commanded to attack or move with an "Attack +X" or "Move +X" action, but it can be commanded to attack with an "Attack X" action (e.g. the Mindthief's "Possession") or to move with a "Move X" action. It can also be pushed or pulled as normal.