It's obvious you're new to Destiny. Let me get you up to speed. Bungie is a dumb company that doesn't allow matchmaking for Nightfalls or raids, but is fine with low level strikes and PVP. They did this in the first Destiny and everyone hated it with a passion. Bungie didn't learn at all for Destiny 2 and pulled the same shit cause they are still a bunch of morons after 3 years. If you want to team up you have to use Guided games which is a -blam!-ing joke and not what people asked them for. It takes tickets and I'm not even sure how to get more tickets, but is free if you are just looking for one extra person. I think the 2nd person with you has to be in the same clan as you? Guided games revolves around clan bullshit. Your best bet is to use a 3rd party website to find people to team up with. It's what everyone else does cause Bungie is -blam!-ing stupid. I suggest you use https://ftw.in/game/destiny-2 as it seems to be the best site to use for groups. You will have to make an account to post your self, but you can also find people that you can invite yourself.

Yes. If you want to matchmake, you need a ticket so you can participate in the guided games. Unless you have one other person in the same clan as you, then you can be the guide, and the game will matchmake one more person with you