They held it for only 20 years. SW is fantasy scifi, ST is realistic scifi; heroes aren't always a defining factor in the latter. With all the opposition from the hundreds of thousands of races and the opposition of the most advanced societies, the Empire would not be able to successfully occupy the Milky way.

And the fighting of the Rebellion at home would drain supplies and focus from any conquest campaign.

ST also has alot of EU you overlook.

No, its a few warlords holding onto that title.

The Empire would not stop at the federation, it would have to take on the Klingon's due to the alliance, and would probably go after the Romulans and other empires. The combined forces would be something the Empire could not avoid and is what would defeat it.

Because it is a way to attack religious theory, and none of the leading characters or races have any omnipotent abilities. It is also based in far developed evolutionary steps, and not magic.