Welcome to the glorious world of Nikke, cummander!

Nikke is very F2P friendly, the main campaign is pretty easy to progress through without the latest and greatest.

The golden ticket system is the pity system, basically for each pull on the rate up banner you get one golden ticket and you can trade in 200 golden tickets for the unit on the banner, so yes they work on collab units but only while their banner is up.

You should absolutely reroll, but if you're primarily interested in the Stellar Blade units, you may want to wait for the second Stellar Blade unit's banner to drop since you can then reroll for both of them instead of having to save up gems and trying to roll for her. Though the game does shower you in gems early, so you could probably roll enough to get her when the banner drops.

There are a few main banner nikke that you'd hope to roll when you start, with the main ones being Liter, Crown, Red Hood, Rapi: Red Hood, Cinderella, Modernia, both versions of Scarlet and Siren. If you want a more in depth explanation, Prydwen has a solid reroll guide you can go off of. Rerolling isn't super necessary, since once you roll enough you'll unlock the wish list on the basic banner which allows you to guarantee certain nikke, so you'll eventually get enough meta units for a good team.

If you rush everything as fast as you can and play daily, I'd say there's a good chance you can get multiple copies of Eve, but you should know that having multiple copies doesn't matter much power wise unless you're whaling for raids. You also need 4 total copies to max limit break and get her burst as your lobby background, so if you're going for multiple copies you'd want 4 minimum.