If I travel to another country on 3 June after dhuhr, then leave on 12 June before Maghreb, will I have to pray qasr? And will I have to fast the days of Ramadan?

The day you leave after Zuhr will not count as travelling if you are leaving from your hometown

If as a result you are travelling for less than 10 days then you will pray qasr and make up the fasts after Ramadan