Because an included file must be opened and parsed by the engine, it adds some overhead. However, the benefits of reusable code libraries often outweigh the relatively low performance overhead.
Should I always end script execution if a file cannot be opened for writing or reading?
You should always allow for this possibility. If your script absolutely depends on the file you want to work with, you might want to use the die() function, writing an informative error message to the browser. In less critical situations, you still need to allow for the failure, perhaps by adding it to a log file.