Why won’t the train go to the depot for regular maintenance

The reason why your planes seem to be slower is because planes fly at a quarter of their listed speed, so sub-sonic planes actually fly at around 240km/h, which is significantly less than maglevs. The quarter speed rule can be adjusted in advanced settings. There are a few other interesting game mechanics surrounding the calculation of vehicle speeds. For the specifics, see the OpenTTD wiki article on vehicle speed.

Whether or not planes are 'worth it' is a purely subjective question, but if your sole goal is making money, then in the absence of competitors, with cities of sufficient size to provide the passengers and enough initial capital to set up the airports and buy the planes, air transport is easily the most lucrative business you can run in the game. It's easy to set up, and require little maintenance, and makes oodles of money compared to the amount you spend maintaining the aircraft. In fact, some players like to set air routes early in the game to make enough money such that they can concentrate on playing with trains later on without worrying about running out of money.

Regarding the risk of crashes, there is one specific case you want to avoid to reduce the likelihood of crashes - large planes landing at small or commuter airports have significantly increased risk of crashing (from 0.07% to 5%), so try to upgrade your airports as soon as you can. A list of 'small' planes that can safely land on small airports can be found on the wiki.

This is the perfect opportunity for path signals. They show the train which routes are available and therefore the parallel trains will only have to stop when the perpendicular path is taken.