How to skip current test script execution of a batch of test scripts when running test script fails?

Point 2 in your post is the best starting point, disabling the "Stop on error".

But once you do that, then you need to modify your tests so that they are "smarter" and will stop execution if they run into certain kinds of errors.  You should add code to detect whether a component is available before you interact with it and, if it's not, raise an exception to halt that particular test case.