What topics should go in the thesis Appendix? I am not sure about some side-topics related to my thesis. During the development of the results I have to rely on some other mehods which are not the main topic of the thesis but since I used them to derive some approximation I then implement in the analysis I think it is useful to explain how this methods works so any reader can understand what I did and also because I spent time learning them.

I was thinking to put these extra-info in an Appendix not to cause confusion in the main topic, but I am afraid they will be considered as off-topics.
If the methods that you are considering including in the appendix were necessary to arrive at your final results, then they certainly aren't "off topic". Without knowing your field of study or your topic of research, it's hard to give a more direct answer than that.

I'm in the social sciences, and we often include mathematical proofs in our appendices in order to save space in the main text (as well as not distract from the substance). Nonetheless, given the importance of transparency, we include our proofs for review by others.