Tomarse muchas confianzas
 

In English?

Tomarse muchas confianzas es por ejemplo cuando alguien te pone el brazo por el hombro sin conocerte de nada, o te coje de la mano etc...

To be overly familiar.

You also say taking liberties.

How about 'to get all chummy'?

Thank you very much . This is the 1st time I hear to get all chummy, I couldn´t say if it means the same as the 1st two.

The meaning is the same. Perhaps worded this way it would be more clear:
He's getting too chummy. (crossing too many barriers too soon)