does it work on laminate floors

NO! Do not use this Bona cleaner for laminate, stone, or tile floors. They made one that is especially for these types of floor finishes. Personally, I’ve been using Bona for everything and swear by them. I use this for my hardwood floors, and the other one for my others. I also use their cabinet cleaner (in a spray bottle) for the light colored wood cabinets in the kitchen and the darker ones in my other rooms which are wood finished. I haven’t used any other products for 7 years now except for Bona!

What is a good mop to use with this cleaner to avoid streaks?

I've been using a Turbo Mop for a while and haven't had any issues with streaking. It could also have to do with the amount of cleaner you're using, sometimes less is more.

What's the best process for cleaning tile floors with this product?

I usually just sweep or vacuum the floors first and then clean them with this product and a microfiber mop. Turbo Mop pads (bought on Amazon) have worked well for any floor type I've used them on.