1)There were tens of students.
Yes it makes sense but you don't often hear 'tens' used in the same way as 'hundreds' or 'thousands'. It's a little strange. More commonly someone would estimate how many people there were to the nearest multiple of 10 and write something like 'There were around fifty students'. Either that or say 'dozens' instead which is more commonly used.
2) Almost grammatically correct. In your example it could be 'Meeting foreigners widens your horizons' or 'Meeting foreigners will widen your horizons'.
'Widen your horizons' means you open your mind to other parts of life, and different possibilities, which meeting people from different countries can definitely do so yes it makes sense.
3) The thing you are trying to express makes sense but the construction 'self-motivate with' sounds very odd to me.
I would write it either as:
Since you do not have a fixed schedule you must (be able to) self-motivate, and do your homework in order not to fail the course.
Since you do not have a fixed schedule you must motivate yourself to do your homework in order not to fail the course.