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.

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.

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.

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