If I order the Student and Teacher Version of Lightroom 5 today (as I am currently studying) - will it be valid forever? Like I probably want to install it on another (new) computer in 2 years from now (when I am not studying anymore) - is that possible?
Yes once you have qualified and completed the purchase you have a valid license for that version of Lightroom with all the normal benefits and privileges that come with it. You have just obtained it at a discounted price.
Keep you License Key in a safe place and register at Adobe.com.