If a unit with the mobility capability is in a space near a terminal but not adjacent ( because a dashed red line separates it for example...); does the unit with mobility controls the terminal or not? I think no... but i am not sure!

Edit: A dashed red line is an impassable terrain edge. It does not block adjacency, whether mobile or non-mobile.

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If a mobile figure occupies a space with blocking terrain:

The mobile figure is adjacent to the terminal, but the space the figure occupies is not adjacent to the terminal. Control of objects is determined based on figures adjacent to it, so a mobile figure in a space with blocking terrain "next to it" would be considered when determining control.

Disclaimer: although this is most probably how the rules as written should be interpreted, and the designers agree on the principles, there is no official and public confirmation.

Further reading:

But if it is just a single red line in between and not blocking terrain, then it won't be adjacent, or am I wrong?

If there is a blocking terrain edge, i.e. a solid red line between two non-blocking spaces (blocking terrain placed between spaces), then the mobile figure is not occupying a space with blocking terrain and normal rules apply. Then in addition to the spaces not being adjacent, a figure/object is not adjacent to another figure/object on the other side of the blocking terrain edge.

Also, it seems I misread the question.

A dashed red line does not block adjacency. It only prevents (non-mobile and non-massive) figures from moving through.

Oh, so for purposes of control, dashed lines have no effect and a figure on the other side of a dashed line has control regardless of mobile or not?

Impassable terrain and impassable terrain edges are ignored/irrelevant for everything except figure movement.

Melee Attacks?

Melee attacks are perfectly fine through impassable terrain edges. It does not affect adjacency.

Melee attacks with reach are perfectly fine through impassable terrain edges. It does not affect counting spaces or line of sight.

Ranged attacks with reach are perfectly fine through impassable terrain edges. It does not affect counting spaces or line of sight. (Reach attack is actually a subset of a ranged attack.)