I would stick to Laravel defaults to make it easier, and use the best practices from Laravel. So convert your passwords, dump the ?query string, use real templates etc.

Sounds good.. I think this will be a rather daunting task, but I'll give it my best shot :)

Can I still use some of the code though? I'm sure regular php functions can be ported over, along with some classes?

Yes you can just use those functions/classes, Laravel is still just regular php :) I usually create a lib or src folder in my app folder and let Laravel/composer autoload that. And I create a helper files for common functions.

I advise getting a single feature working first on a single route. e.g. if your app allows you to manage users get that bit working first, you'll soon see then what code might need to be shared across the models/controllers and what needs refactoring.

There are some great tutorials on https://laracasts.com that are good if you are starting out.