Arknights

You may purchase Originite Prime in-game for real life money, although this is not needed to progress the game at all and is mostly used for when you wish to buy in-game costumes/skins.

The game does have a option to spend one Originite Prime (Premium currency that can be earned through gameplay quite easily) to refill sanity (Energy), though this is often simply a waste with how much Sanity Refills the game gives you for free during events and casual play.

There's a badge system in game that is purely aesthetic and serves more of a tracker of what you should do next instead of a way to show your prowess.

Anhilations are maps that often take 10+ minutes to clear for currency that can be used for rolls, though rolling is not needed to progress so this is more of a way to self-indulge.

The game does have a energy system called Sanity, though the game often gives you refills you can use at your discretion so you can return to playing at a convenient time for you.

There's a in game system where players can help each other out, but it's such a minor part of the game it can't affect anything out of it's own bubble.

Technically, yes, but not directly, you can use Originite Prime and convert it to Originium which you can then use to roll on banners for units, the catch here is that after a while the rates for the 6* (highest rated units) get higher the more you roll, and accumulating rolls is easy, so if you skip previous banners you won't ever have to spend a cent to get what you want.

Yes, but the rewards aren't anything that will greatly help you so there's no obligation to get it.

There is a option to sign up for a monthly pack which is at a reasonable price for what you get.

Daily reward quests span a wide variety of content in the game.