Entire encyclopedias have been written on the subject of why Rome rose and why it fell, and the process was so intricate and controversial that you'll probably never get a definite answer here. Opinions vary on whether or not conquest helped the Empire by bringing in booty and subjugated peoples to be assimilated or hurt it by overextending its transportation, communication, agriculture, and military systems. What we know for sure is that expansion slowed down with the Empire; much of Rome's territory at its height was actually conquered by the Republic or by Augustus in his early reign. And the Empire was still fine at the time, during the reigns of "good" emperors like Marcus Aurelius and Trajan the empire retained its money and power, and defeated enemies like the Marcomanni, the Quadi, and the Parthians.

In terms of your second question, aside from extra people to tax and eventually recruit into the auxiliary, slaves were a large part of why Rome conquered. Rome relied heavily on slaves for public works, and they needed a lot: Josephus recorded tens of thousands of prisoners sold into slavery in Vespasian's Judea campaign alone , and remember that Rome was involved in not one but three Servile Wars, each with tens of thousands of revolting slaves. Average Romans were not expected to fight in a gladiator ring or work on a road; that was the slaves' job. If there were no slaves, there were no public works, and so when the Romans couldn't conquer they had to marry slaves instead. Did this contribute to the fall of the Roman Empire? I have no idea. But it was a reason to take a city, and keeping a healthy workforce certainly outweighs administrative costs.