Upon my arrival to a country which is not mine.. for the first few months and before knowing that I'm going to stay in this country or not, can I pray (Qasr) - Traveller's prayer? If I can, how long (i.e how many months) can I pray Qasr?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Whoever travels in a lawful journey and its distance is 80 K.M or more; he may shorten and combine the prayers; i.e., shorten the prayer of four Rak'ahs to two Rak'ahs, like Thuhr, ‘Asr and ‘Isha prayers. If one stays during his trip in a given place for some affair, then he may continue to shorten the prayer and may combine between Thuhr and ‘Asr and between Maghrib and ‘Isha when he needs it as long as he has not determined the period of staying. But if he is in a place where Muslims pray in congregation, then he should pray in congregation with Muslims. Allah Says (what means): {And establish prayer and give zakah and bow with those who bow [in worship and obedience].} [Quran 2:43]

On the other hand, if the journey of a person extends to a long period as it is the case of students, and those who work outside their permanent habitations, then one has to perform complete prayers [i.e. without shortening them]. This is to be in conformity with the view of all scholars, although shortening is allowed according to some opinions.

Allah knows best.