Are all vBulletin styles mobile optimized? Or, I have to pay some more to do it? I am confused right now. They say they responsive but I see a lot of extra packages that specifically say Mobile or for responsiveness.

Yes, they are optimized by default. The extra packages which you see are basically if you need an app for your site then those are for that. Otherwise, a simple vBulletin script is responsive for all devices.

All latest versions and themes of vBulletin are responsive by default.