From my understanding so far, I think that a quasi-static process is one where the system is in thermal equilibrium with itself as well as the surroundings and the process takes place infinitesimally slow. So, my question is are these different processes reversible? Are all quasi-static processes reversible?
If I remember my thermodynamics correctly, all reversible processes must be quasistatic but the opposite is not the case.
For a process to be reversible, the entropy produced must equal 0. However, some quasistatic processes may produce entropy even though the system is in thermal equilibrium and the change occurs infinitesimally slowly. I recommend you to look for some examples of this online, there are plenty! :) A place to start would be the Wikipedia article on quasistatic processes, whilst this https://arxiv.org/ftp/arxiv/papers/0911/0911.5010.pdf ("Are all Quasi-static Processes Reversible?") might be a bit more thorough.
In addition to being in thermal equilibrium, the system must also be in mechanical equilibrium with itself as well as the surroundings, which generally means minimal pressure differentials.
As @Samalama pointed out, all reversible processes are quasi-static but not all quasi-static process are reversible. An example is a quasi-static process involving friction (e.g. piston/cylinder friction). Although the process can be carried out very slowly friction is dissipative, thereby generating entropy.
Hope this helps.