I want to buy the Student Version of Lightroom 5 (No Cloud).
Can I update this Student Version to Lightroom 6 when available? If yes can do I have to buy the full student version again or can I as well by the normal update Version if no longer a student?
Yes you can upgrade through the regular process. Your LR 5 is the same program as the regular application you just got the license key at a discounted price.
If you still qualify you can go through process of purchasing the Student Version which will more or less be around the same price.