You actually can't use ため for all of them.
ため specifically connotes that the second action is under the control of whoever performs the first action. Your first example is a good case for this: you are going to Japan, and you are in control of whether or not you work (theoretically - if you phrased this as 'to find work', you wouldn't be able to use ため).
The alternative to ため(に) is よう(に). よう specifically connotes that the second action isn't under the control of whoever performs the first action. Your second example is a good case for this: You study hard and hope that you get good marks, but you're not the one controlling whether or not you get good marks (at least directly).
With verbs of motion (行く、来る、戻る, etc) you can use the 連用形 form of the verb plus に directly - for example, 取りに行く 'go in order to get'. You can't separate the purpose from the motion verb, though - *働きに日本に行く is ungrammatical.