welcome back, looks like you have a pretty decent character and you're on your way to a sweet end-game character :) lemme try to help, but rem that there really aren't good/bad options its all about playstyle, what's fun for you, etc. etc.

(btw now that ive started school again and dont have time to play i have a notepad for memory too lol)

---My goal, first of all, is to grow enough to break all the challenges. Fast.
---For that, it's okay to buy energy to save time.

If that's what you want to do, that's all good. Have fun! It's great to support the games you enjoy. You'll find running the vanaduke mission is one of the best ways to make crowns/energy. General Tips: Play through the mission (some people speedrun, others don't. It's definitely better to run through the mission with friends or other players that know what they are doing.) The mission will net ~8k crowns every run + 2k crowns if you include the token. After 30 tokens, go to Bazar and use the tokens to buy a piece of random armor. Then sell the armor to a nearby vendor for more crowns (I think 30k crowns).

---What I figured out :
---1. It's time to do 8-2.
---2. It has 34,000 crowns and 200 energy.
---3. I have 37 Shining Fire Crystals.
---4. My equipment settings are:
---Weapon: Fusion Blaster, HEAT 5Lv, 4 (I think Arcana was the target)
---Weapon: Strike Niddle, HEAT 5lv, 4 (I think the Blitz Needle was the target)
---Armor: Miracle Hood/Miracle Cloak 5lv, 4 (I think Chaos set was the target)
---Shield: Wise Owlite Shield 5lv, but cannot find it in forge.
---Bomb: For the achievement I need it, but I don't have any.

Yea work through your missions. They aren't very fun at times, but the end game is so good. I'm really glad I got through some of the grindy missions. Ask anyone. The end game is way better. You aren't too far from the endgame content if my memory is correct. That's a decent amount of crowns and energy for a casual player. You'll find out soon that it takes lots of crowns/energy/resources to craft gear. Don't buy gear, its cheaper to make it if you don't mind heating.u

Heating might have changed since you last played. Killing monsters bring you heat. At the end of the level, the heat transfers into your weapons,armors,etc. Press "U" (by default, I think) and heat up your stuff. Recipies will tell you what heat level things need to be. *BTW* as i'm writing this, join the discord and you can ask all these questions whenever you want. 4* requires lvl 5 heat and 5* requires lvl 10 heat.

Note: Maxed Heat 4* is strong than a no heated 5*. (But since you are just trying to grind out the missions and stuff dont worry too much about that)

Your gear is actually really good. Work towards the 5* Choas set. (One of the best sets). Work towards the 5* Blitz (One of the best DPS weapons). Ditch the gun and bomb for a good brandish sword. You only need 2 weapons 5* for missions. Later you can experiment and figure out if you like the gunner playstyle (2 guns), mixed, bomber, etc. etc. (End game is really enjoyable so you kinda just keep playing fun end game missions working towards better and more gear so don't worry too much about "this gear set needs to be perfect")

---What I remember :
---1. To get to ★5, I need a recipe. But I don't know how much more HEAT I need.
---2. At 8-2, my damage was too weak and quickly died, so I quit the game because it seemed to take too long.
---3. I remember I was suffering from a lack of crown. I have the memory of buying energy for this.

Yep. Need 5* gear to finish all missions. The spiral knight wiki is your friend here! Look up your gear and from there on the wiki you should see "tree" of where you can go from there. Like I said, that gear correlates to the "Choas Set". You can find all your recipes for the armor you have and the blitz gun in the Hall of Heros. (Far Right At Haven)

---Questions :
---1. First of all, what should I do? I have not enough damage to clear 8-2, and I die so quickly.
---2. I know the 5 recipe is 25,000 crowns, but where do I get it?
---3. Is it correct that HEAT needs 10? Where can I get it fast?
---4. I don't know the difference between expedition and clockwork needed for the challenge.
---5. Are these questions enough? Are there any other tips?

Ask people for help. I'd help, but I have classes now :(. Join a guild maybe. Best way to make crowns is to play vanaduke. If you haven't yet gotten to the vanaduke mission ask people for invites. Alternatively, you can run jelly king. Make crowns. Turn into Energy if needed to buy orbs of alchemy.

In order to level up your gear you need heat. In order to craft the next tier of armor/weapons/etc. you need the right heat level of your armor/weapon/etc. + resources like orbs of alchemy. There is a great guide to finding orbs of alc in spiral knights just look it up. In most cases tho, you can just buy a pack with energy. Keep in mind that the first 5* set is always the hardest after you climb this hurdle the game becomes much easier.

Again, get heat from killing monsters. When you descend to the next level in a mission, the heat transfers to your gear. When your gear reaches max heat, you can level up the gear using the heat. (Press "U" by default). Can't do this during a mission btw.

"I don't know the difference between expedition and clockwork needed for the challenge."

Idk what that means. The Clockworks is the game work. There is something called the arcade which has always changing game levels.

Just ask around in game, on forums, on the discord, wherever. People can be really helpful.

#1 tip - make friends in game, its great if they are high leveled and can help-- just be nice and ask :)

Good luck