How to play solo or find a party?

I've had no issues up until the first 3-2 dungeon but by this point it's clear the game was made to be played in a party.
The issue, though, is that (apparently) close to no one is playing the game. I can't seem to find anyone either hosting nor joining the missions I'm doing, no matter how much I reload the party finder nor iddle on an open party.
I'm not able to finish this mission by myself the way I'm playing so here I'm am requesting either tips on how to solo (besides the usual "git gud") or finding people to play with.

Same dude; managed to log in with my Steam account. Here's some input:
A. Might try that, though it's not something I'd like to abuse. Gonna try it with this particular mission that gives some armor and try to survive by myself again afterwards.
B. Just posted a request here in the guild recruitment forum, as well as requested invitation to some I saw.
C. I'm using the mission-issued gear, as I don't either have better recipes nor the coin to buy new ones. I'm not missing attack, as you seem to imply. My issue is my low defense, as I've been using the same armor (0★) for most the game. Recent dungeons throw more enemies than previous ones and, as I'm by myself, even with dodging and blocking I end up acting as a pinball ball.

First, don't wait for an answer through the Guild Recruitment forum. I'd recommend asking someone in Haven for an invitation into their guild. You want someone who seems nice, not someone who seems rich or powerful.
Second, which rank mission are you currently working on?
Third, even if you use only mission-issued standard gear, you will soon receive a massive upgrade from 0 stars to 2 stars. Then you will have Calibur and Blaster (and Blast Bomb). Your killing power will skyrocket. So be hopeful. :)
Finally, your play style will not really change, because Calibur and Blaster are basically more powerful versions of the 0-star weapons. So, while you wait for them, practice the following play style.
- Charge your sword. While you are charging, you must keep moving. Never stop. As you move, try to cover as much ground as possible. For example, it is better to run in big circles than to shuffle back and forth between two positions.
- Run toward a monster, release your charge, and run away. Then go back to Step 1.
With this play style, you are still vulnerable to projectile attacks, but you are essentially impervious to melee attacks, as long as you have room to maneuver. Try to make it through a melee-heavy level with taking any damage at all. I'm not kidding. You can do it.
This is how most experts play Spiral Knights. Powerful weapons, weak armor, lots of dodging.

1.
Oh, I've also tried that. The thing's, even changing channels, there never too much people there. It also happens half of them are not on a guild and half of whats left is AFK :I
I still haven't found anyone that answered my whispers.
2.
Just finished Rank 3.
3.
Yup, already got them. Haven't yet tried them, though.
4.
I'm already kinda familiar with the hit and run, don't stay put play style but still I can't always manage to keep it up when there's 8+ enemies and I'm all by myself.
I'm not using the charge attacks at all though, I must admit, as so far they've only appeared too slow and really easy to miss. And even when it hits it doesn't seem to do much more than a regular attack. I will give them a second chance, by your suggestion.

General advice, if you're asking for help with a mission, you're probably better off saying the name of the mission, in addition to the mission number. There are like 100 missions at this point, and most people don't know the specific number of individual missions outside of special missions like Built to Destroy and King of Ashes. As a really old player, saying 3-2 is mostly meaningless to me, but I do know Shadow of the Beast refers to the Gloaming Wildwoods and the lair of the Snarbolax because it's a unique area.
That said, according to the wiki, most of the 3-2 missions feature pierce weak enemies and enemies that are dealing pierce damage. If you can, perhaps try to get your hands on a Flourish. For armor, I recommend the Wolver set. It'll cost more than your standard cobalt, but it'll work out better in the long run. They should be available in the Hall of Heroes.

I agree with Traevelliath about how to ask for help.
I also agree that you might want to invest in the Wolver set or some other semi-offensive armor. See my armor guide for more information. While the mission weapons are good-but-not-great, the mission armor/shield is some of the worst in the game.
I don't agree that you should get a Flourish right now. It's a good sword, but it's a low priority for you. If you're into swords, then you might want to check out my detailed sword guide. In particular, if you want offense that doesn't require mastery of the game, then consider the Brandish lines (Combuster, Acheron, etc.).

3. Yup, already got them. Haven't yet tried them, though.
I don't understand this part. For what are you waiting? Are you trying to fully heat your 0-star items? Just stop. Soon you will sell them for 1 crown each, because you will never use them for anything practical.

I had just got them when I wrote that so I hadn't had the chance.
They obviously do more damage but I still don't see the charge damage doing more than 150% of a single normal attack. I tried using it for a while but it just doesn't seem worth it.
Haven't played for a few days so I've still not checked the Wolver set nor the Flourish weapon.

That's fine, that you haven't tried them. We're not here to boss you around. :)
You are right that the charge attack does not generate much higher numbers than the regular attacks. But that is not the point.
The point is that the charge attack knocks the monsters away from you, giving you room to run around and charge your next attack. The monsters literally cannot melee against you, because at any given time you are either (A) far away from them or (B) unleashing a big attack and interrupting whatever they were doing.
In the case of the Calibur line, there is a second point to the charge attack: Because you spin around three times, a single charge can hit a monster up to three times, thus doing quite a lot of damage. This tactic works best against stationary targets (such as gun puppies), knockback-resistant targets (such as giant lichens), and targets pinned to a wall.

As you wrote, charge attack does have quite some knockback. I mean, with Calibur it does. With my previous weapon there was either almost none or just no knockback. With calibur it really comes in handy by getting all the enemies off you and, as it spins, it's quite harder to miss. So thank you very much for the tip.
Also I'm noticing the small ATK buff from the armor and it looks quite cool too; so thank you too, Traevelliath, for your advice.
Right now I'm pretty satisfied with my gear, thanks to both of you :)
You're right that the game was designed for party play. And you're right that the party finder is pretty much useless (at this point) for a low-rank knight trying to work through missions. But here are three ideas:
A. Stand in Haven and ask for help. Be calm and dignified about it. No one must think that you're begging, because players don't like beggars. You might make some new friends.
B. Join a guild. Your guild mates should help you, even if they take turns.
C. We could talk about your equipment here. Perhaps you've chosen weapons that make the game hard, or perhaps you're using the wrong damage type on the wrong monsters.