1.We need to see the stacktrace to help here. A null pointer exception can occur everywhere.
2.Make sure you have latest versions of Eclipse and TestNG installed. If you still have this bug afterwards, please consider uploading screenshots and/or code.
3.Right-click context menu shows up „Run as TestNG Test“ or “Run as TestNG Suite” respectively if you do it in the project explorer. In the Editor, you can still at least do the former given you have a test class open.
Another way is using the “Run configurations“ which you can access using the drop-down arrow aside from the green play button in the toolbar. There you can select TestNG and define a suite, class or method to run. There you can also define parameters that are given your tests if you’re using the @Parameters annotation. The entries you do there stay so that you can execute the same tests later on with only one or two clicks. Also if you use right-click context menu the recently run things show up there too.