I can not install the Application Builder V5.0.1 under LabView 5.1, so if I want to use Application Builder, do I have to buy the newer version at first?
That cannot work. The AB must be always the same version as the LV version. If you have bought the Application builder once, you can ask for a free upgrade (I'm not 100% sure). Call NI and ask if you can have an upgrade of the AB. The question is if they give you still an LV 5.1 AB!