I also have a general question. This is my first Diablo game and it’s 3. I am wondering what you do after you beat the campaign. Is it just running dungeons with people and such?
Yes. Once you get to 70 (on your first character; with 'alts' (further characters, after you've heard your 'main'), a new option called Adventure Mode opens up. There are several activities for endgame: bounties and nephalem rifts (always available, and always at the difficulty level you've set when opening that 'instance' (the game you're in an that moment), and greater rifts (which have their own mechanic for pushing higher and higher, along with their own unique reward system (blood shards that can be gambled at Kadala, and powerful legendary gems with their own affixes).
There are a lot of resources available online to guide you towards and during endgame. You might want to riffle through the YouTube channels of, say, Rhykker, Raxxanterax, Rob2826, or one of their colleagues. I personally like Raxx's content a lot.
EDIT: 100 points extra for your username, LOL. Even in-game, hahaha!
After campaign you start doing rifts where you get greater rift keys.
In greater rifts you get legendary gems that you can upgrade after finishing a greater rift.
End game is to see how high you can finish a greater rift. Max is 150.
Do rifts, greater rifts and bounties to upgraded your gear. You want ancient and primal ancient gear so that you can enhanced it with gems to get higher main stat for more damage. But a normal piece with the right stats is better than a ancient one without it.
If you by any chance made a seasonal character, you can do your journey to get a free set for your class. After that focus on doing the altar of rites.
To your first question, it's called a Treasure Goblin. You chase him, usually through other enemies, and he drops items and stuff when/if you kill him. To your other question, yeah pretty much
Do you have a puzzle ring equipped? The affix on that means a treasure goblin follows you around picking up junk and common items. After it picks up enough it will drop a rare item that has a chance to be legendary