@Aggelos-Minoudis ...may be there are a couple of things you need to care about:
I'm not sure, you strictly have to use gpx V 1.2 file format to transmit to a Garmin XT2. May be gpx V 1.1 is working good enough.
You also need to know: if you export a route from MRA-Routeplanner as gpx file - this file will contain a route AND a track. If you import this gpx into Garmin XT2, both will be imported. You can disable in XT2 afterwards to display the track. I believe, then you will get the ETA.
If the Navi is going to route you often back to starting point - this can happen, if your first route point is to close to your current position. If you just switch on your Navi and start driving immediately, it could be the navi did not have enough time, to get enough satellites to calculate the route - and did not notice, you have still reached the first route point. Then it will navigate you always back to the first routepoint, as long as you really have reached it.
It's recommended to place the first route point some 100m away from yor home or hotel (current position) along the planned route down.
About Android Auto / Carplay I can't support you, because I don't use such a device (I don't like it).