Won't the Streetcar be constantly stuck behind a double-parked car, a down tree branch or something? It can't go around anything!
The Portland Streetcar also operates in mixed traffic just like the Columbia Pike Streetcar will. When you add together every single service disruption, no matter what the cause in Portland's first two years of service: mechanical problems, power outages, the driver not showing up, passengers getting sick, police and fire activity - it adds up to less than 1% of service [source]. It's a reliable system.
What happens when there is a fender-bender, double-parked car or delivery van blocking the Streetcar?
You keep a contract with a towing company. The driver radios dispatch who calls in the tow. Drivers quickly learn not to double park in the way of the Streetcar. Tracks in the street make a very effective no parking sign.
What happens if the power goes out?
It depends on how extensive the power outage is. Streetcars systems are generally designed such that each traction power station is fed from a different portion of the electric grid and the system can function even if one of those traction power stations goes down. So in a fairly localized power outage, nothing much would happen. In a more extensive outage, the streetcars all have enough reserve power on-board to get themselves out of an intersection if they are in one. Until power was restored additional buses would be called in to take up the slack. That is assuming the weather conditions that caused such an outage aren't such that the buses can't run reliably either - generally a storm strong enough to have knocked out power to that much of Arlington will have caused enough other damage to halt bus operations as well.
What happens if a Streetcar breaks down?
The next Streetcar to come along simply tows or pushes it back to the maintenance yard. This should happen infrequently, though as Streetcars tend to be more mechanically reliable than buses.
But what if something REALLY major happens that completely shuts down part of the Streetcar route like a huge fire or something
A "bus bridge" would be brought into to detour around the obstacle, just like MetroRail does when their is a major issue that shuts down a part of the line. Some buses would even already be there since the Arlington Streetcar routes on both Columbia Pike and through Crystal City are also generally bus routes.