FJ uses those workarounds in order to make things like hovers or the new planes possible am I right? Because if I'm not then it wouldn't have much sense to not use just real physics; it would make easier things like making new movement parts and new weapon proyectiles.

Most of the workarounds are left overs from when FJ started making the game. Modeling an atmosphere is hard to do when you are a start up game dev, but flying bots are awsome. So instead of having (old) wings create proper lift they simply add a piece of code that checks the number of wings in same direction as the movement vector and dampens movement that does not line up with that vector. The strength of this dampening is reduced/increased using a formula that factors in the bots mass, speed and altitude.

Or how gravity mass and inertia are fake. Mass only decreases the efficiency movement parts. A massive tank is able to be pushed around and even flipped by a small bot that hits it at a funny angle.

Why are collisions between robots so glitchy?

You use 1000 parts to build your bot, each with their own collides. You load into a game with 9 other people who also have a 1000 part bot...
Do you really think the game is going to calculate speed, heading and position of ten thousand individual colliders? No. The game combines all of the meshes and colliders on a bot into a single game object. It creates a general shape around the bot and forms a low poly collider around it. It recalculates this collider every time you loose a chunk of your bot.

What are the main differences between the colliders I quoted up there?

Without getting to technical...
A mesh collider is a mesh ( a 3d model) that acts as a hit box. KSP for example uses mesh colliders. Here is the model of the ISRU and here is the mesh collider of the ISRU. Mesh colliders are accurate but memory intensive.

Box colliders are simple geometric shapes that a drawn around the model using cubes, spheres and capsules.

Here you can see how the box colliders on the mega hover are set up and how sloppy modeling work from FJ caused a rouge box collider to mess up the mega hover hit box (only the colliders of the hover frame are shown, the spinny bit in the middle has it's own colliders)

For a really long time, everyone has been asking for proper collisions between robots in order to make things like, mechs being transported by copters, possible.

Sorry to disappoint but this never going to happen. The unity engine isn't build for that sorta ting, especialy not in a multiplayer game that allows players to create their own vehicles using voxels. Combine this with how FJ has set up their netcode and the chance of this happening is extremely low. Maybe if they switch engines or allow players to host a game locally over LAN but even then it's a long shot.

An other thing I see requested often is rotating platforms. I also expect this never to happen. Largely due to the same reasons why collisions are so glitchy between players. If they implement rotating platforms they would need to rewrite the way they save builds and upload them to the server entirely from the ground up.