www.wysiwygwebbuilder.com

For some reason file extensions (.php & .html) are not being published on my website—hence links to internal pages can’t be found. To correct this I manually edited the script on site to link the pages by adding the file extensions. Is there something that needs to be done with the program to make this publish correctly?

If you mean the links are without the file extensions then you have probably set the option:
"Hide file extension for internal links (use with caution!)" in Tools > Options > Publish.
Unsetting it and republishing should solve the issue.