You draw one card for each Dragon you controlled that attacked, even if some of them left the battlefield before The Ur-Dragon's triggered ability resolves.

You may only put one permanent card from your hand onto the battlefield, no matter how many Dragons you attacked with or how many players they attacked.

If a Dragon you control enters the battlefield attacking, it won't cause The Ur-Dragon's last ability to trigger.

The Ur-Dragon's triggered ability resolves after all attackers have been chosen. You can't attack with some Dragons, put a creature card with haste onto the battlefield, and then attack with that creature. Similarly, any "whenever a creature attacks" abilities of the permanent card you put onto the battlefield won't trigger.

Three eminence abilities are triggered abilities. That creature must be on the battlefield or in the command zone as the trigger event occurs and also as the triggered ability resolves. If the creature is in an appropriate zone as the trigger event occurs but leaves that zone, the ability won't do anything as it resolves.

Notably, if your commander is on the battlefield and its eminence ability triggers, but it's put into the command zone before that ability resolves, that ability won't do anything as it resolves. This is because an object that changes zones is considered a new object.