What happens if two different elementary particles with different charges collide? For example, the up type quark and electron, or down type quark and up type quark. What will happen then? What will be absorbed or radiated? In the end, what kind of particles will turn out? Will it annihilate?
These questions have been bothering me a lot for several days now, but there is no answer on the internet. Please answer, and I am even more concerned about what the Feynman diagrams look like in these cases.
 A: What happens when particles collide? What particles can collide and what not? These questions are answered by knowing the Lagrangian of a theory, which is a function that tells you the dynamics of your objects. From the Lagrangian one can obtain the Feynman Rules, with which one draws the Feynman diagrams. Our current best theory is the Standard Model, and from its Lagrangian one can derive the interactions. As far as we know, an up quark and an electron cannot interact directly with each other, meaning that there isn't a vertex where an up quark and an electron interact with each other. They can interact via the exchange of a Photon or Weak Boson:

If this is what you mean by "collide" (which, despite many experiments being called "colliders", isn't a term that most theoretical particle physicists use), then this is your answer.
Up quark and down quark, that's a different story. In the SM Lagrangian, one can see that there is a quark-boson-quark vertex, meaning that two quarks can annihilate and produce a boson:

This boson will quickly decay into other particles. Which ones? The ones allowed by the Lagrangian! A lepton-antilepton pair, or an up-down quark pair, for example.
Ultimately, electric charge (which seems to be what you're interested in) is a number that must be conserved at each vertex, but that doesn't otherwise tell you what vertices are allowed and what aren't: you must study and understand the Lagrangian of your theory.
