1. I've always been intrigued about how that works -- when the wheels touch down when they're not aligned with the runway.
You need to apply downwind rudder PDQ to straighten the fuselage & therefore the undercarriage with the runway axis.
2. Second, is there anything to be worried about when you touch down at an angle?
Worry is perhaps not the correct word. If the undercarriage has been designed and stressed to do this, then it is allowed. There are interim techniques to reduce the stress, e.g. impart a little side-slip in the latter stages, but each a/c has limitations on there degree of side slip.
What is important is to straighten the longitudinal axis of the a/c. The wheels are pointing into wind; the a/c, due to the rudder, wants to head off into the wind. If you do nothing, or are too late in removing the drift angle, you will go off-roading PDQ. Is that a worry? NO, it is an alert that you need to be sharp about it.