Can I push the train of 60052 We more like to push trains with hand. There were old ones, like the train of set 2741, where when pushing the engine, the contact became loose between the axis and the cog wheel.
Can I count some similar damage, if we push the engine of 60051 (and 60052)?
I would not recommend pushing the motorized train base for extended periods of times. When you turn the motor, it will generate electricity. Unless that energy has somewhere to go, it will turn into heat. It's probably not an issue to do this a little bit for short periods of time, but I wouldn't do it a lot.

If you wish to make your train a push train, you could replace the base with another non-motorized base.