I would like to ask what is the most common phrase in English which allows you to express the fact that (for example) only ten minutes remain to the train's departure. Is my version O.K.? Thank you.
There are ten minutes to the train's departure.
Your train leaves in ten minutes.
The train leaves in ten minutes.
Your version is okay, but not idiomatic. You could say
There are ten minutes until your/the train leaves.
(The your in the above sentences applies to when a friend is telling you. They would probably most often use your, but the is also possible. Both give definite references to train but your is more personal.)
There are several ways. You could say:
There are ten minutes until the train's departure.
There are ten minutes until the train departs/leaves.
or
The train will be leaving in ten minutes.
until is a better preposition because you are going up to a specific future point in time.
In AmE, the informal way to say it would be:
The train leaves in ten minutes
More formally, it would be:
The train will be leaving in ten minutes
Your version is fine, I would use that in a formal setting. If I was with friends, I would say that "the train leaves in ten minutes".