In Portland, a far too frequent cause of MAX (the light rail) service interruptions is due to car/train collisions. See the following links for a small taste:
Sounds like a poor design, most places will have people boarding from sidewalks or a raise area.
As for the 2nd, people run into stuff in the cars all the time. Around 50-100 people die each day on US roads. And in the story you mentioned only the people in the car were injured, nobody on the train.
It's not really comparable to heavy rail in terms of speed or capacity. You can fit 1,500 people into a single NYC subway train, way more than any light rail system in existence, and the express trains go way faster than any light rail because they don't have to worry about potentially hitting stray pedestrians, bikers, or vehicles. NYC subway cars will go up to 55 mph going express or in tunnels. At-grade light rail simply can't go that fast, or even if it could, it wouldn't do it because it's unsafe.
Select-bus service (that is, buses running in dedicated lanes) is about as fast as at-grade light rail, and significantly cheaper to construct. NYC has been going in that direction for awhile. Building at-grade rail is just a complete non-starter. The city already tore out all of its above-ground rail a long time ago for a variety of reasons that persist to the present day.
