That's unfortunate. Most of the issues you are having are PHP issues and truly have nothing to do with LSWS. LSWS acts as a front end to PHP and if you do not configure PHP correctly, or use modules that are compiled incorrectly, or use cache optimizers like XCache and do not install them correctly, you will get 503 errors through LSWS. Basically, LSWS is passing on the error information from PHP in the form of 503 errors.
To fix them, you need to isolate what is wrong with your PHP installation.