1a. It doesn't matter which language is used to access the database, as long as the queries are MySQL.
1b. You'll need to write the plugin yourself since it will be custom to a particular database.
1c. That might work but would probably look ugly, and the site will probably be sluggish.
2. The theme should be the last thing to worry about. Getting the customer database in order is much more important.
3a. See 1a.
3b. Depends on whether your dad values functionality (QuickBooks) over appearance (WordPress). (Yes, I know that's a blasphemous statement to make here, but WordPress is often not the best solution for a website.)
4. You seem to think this will be a turnkey project with WordPress; it will not. If you go the WordPress route, your dad will most likely need to hire someone to write a custom plugin (maybe two) and to heavily modify a theme.
If QuickBooks could work for your dad, he should probably try that first. If that doesn't work out, then you can persuade him to go the WordPress route.