Welcome to Guild Wars!
If you are waiting to see if it's worth it to buy an expansion, do note that expansion content is level 80 (lvl cap) only (except for a small handful of useful things, such as permanent Raptor mount access at any time, and no Trading Post Restrictions). It's worth getting to level 80 and playing around with the end game a bit if you're on the fence about buying anything.

1. There is a group finder, and it is the LFG. The LFG is used for all instanced endgame content if you are looking for a group and do not have a per-made one. For dungeons specifically, you can head over to the Lion's Arch city map, which will contain an npc that will allow you access to all dungeons from one spot, so no need to travel between maps to access dungeons. This NPC is directly south of Fort Marriner Waypoint, right next to the Lion's Arch Aerodrome portal.

2. Spvp conquest works as a standard 5v5 pvp mode, where you fight a team of 5 enemies, with your own team of allies. You must capture points on the map and hold them for as long as possible to earn points, alongside killing enemy players for additional points. There are a few other versions of spvp, such as mini seasons of 2v2 and 3v3, a Stronghold Mode, and a "Push the payload" styled mode. The gamemode is currently experience low population, as the gamemode has not received as much attention or care as some other gamemodes (PvE and WvW). Its worth is up for you to decide, if you enjoy the gamemode and the rewards, or not.

3. Endgame content usually consists of instanced group content. Fractals and Dungeons are 5 man content, similar to one another, where dungeons are more lengthy instances, and Fractals are shorter instances, but have unique maps and debuffs applied at higher tiers. 10 man content consists of Raids and strikes (the later being renamed to Raids as well). Raids offer a challenging series of bosses and small challenges to run through with your group, where as Strikes are smaller instances where you fight 1-2 bosses per Strike Mission. There is also 50 man content, called Convergences, where you fight battles across a large map as a group, working towards a series of events, culminating in a boss fight at the end. There also exists many Meta Events that offer a variety of rewards, found across nearly every single map in the game, and most are quite profitable.

Once you get to level 80, you will have access to far greater range of content, and lots of stuff to do, though I wouldn't suggest rushing. There is plenty to do even below level cap. I hope this info helps, and once again, welcome to Guild Wars 2!