1. Explaining Destiny 2 PvP can be confusing but I'll give it a try. I'm by no means a PvP guy so things might not be 100% right here.
- 3 Playlists in the Crucible that are selectable at anytime. (Quickplay, Competitive, and a third that will cycle weekly between a few different gamemodes)
- Quickplay is your casual experience. 6v6 Deathmatch and Control. It affects your Valor rank. Losing doesn't hurt you, completing a match gives you small amount of Valor points, and winning gives you a bit more. You get more points if you are on a win streak (capped at 5 wins). This is what we mostly play because it's the least sweaty way to get our weekly reward for playing PvP.
- Competitive is 4v4 with basically bomb plant/defuse and a game mode where your team has like 10 lives total or something. I can't speak much on this though. This affects your Glory rank. You actually lose glory points when you lose, there's the same win streak system as Quickplay though. When you reach a certain Glory rank, you will be able to get a good weapon they design specifically for the hardcore PvP players. Very few people can do this so its something to chase for higher end PvP players.
- The last playlist will rotate weekly between free for all (1v5), doubles (2v2), Mayhem (Supers regenerate wayyy faster, you'll basically have a super for every life), and Iron Banner (6v6) which comes once a month and they all last the full week. For Iron Banner, a vendor shows up and sells a full armor and weapon set per season. Basically its a reason for all of us to bite the bullet, get a full group together and actually enjoy a bit of crucible as a Clan.
There is also Trials of the Nine which is 4v4 and you get rewards for winning 5 in a row and 7 in a row and it's the sweatiest sweat fest in Destiny 2. Hope it doesn't sound too exciting because they are removing it for a few months after Forsaken drops. It wasn't too popular so they are going to rework it a bit before bringing it back.
2. Being in a Clan has a few perks. There are a few very basic things like increased money when you kill certain enemies, better chance of materials dropping, that kind of thing. Also, there is a vendor who will give you gear the 1st time the clan completes something that week (meaning if we finish the raid, crucible, strikes, or trials for the week, she'll give you gear even if you didn't get on and play any of it.) Basically, you'll get a few free pieces of gear while we are all playing. And lastly, I check my Clan roster more often than my friends page to see if people are on. It's a separate list so if you join the clan you'll be able to see when any of us are playing without having to add us to your friends list. That being said, if we see you on enough you'll probably get a friend invite regardless.
3. Base game overall is pretty good, Curse of Osiris overall is pretty bad, Warmind overall is good. A few good and bad things in each of course.
As for your questions.
1. PvP might be tough at first because you won't have many of the good guns. The better your collection gets, the more fun you'll have. And like I said earlier, there are events like Iron Banner, Mayhem, and double valor points weekend that'll cause a lot of us to get on and play.
2. Forsaken will allow you to bring one of your characters up to the level required for Forsaken (I'm not sure if it will give you gear that is strong enough for you to survive though.)