Depends what your aims are I would say. If you plan to work or study in a particular country, or in a particular part of that country, you could pick a teacher from that area. Really though, although English differs a lot internationally, fundamentally correct usage is more important than accent or minor local vocab differences. Do you have difficulty understanding your teacher's accent?

Being understood is the goal. If your accent interferes with being understood, then take pronunciation lessons. Sounding like a native speaker is very difficult (almost impossible) and not needed.

You will have to decide if the accent is a problem. It may be of no particular consequence.

Depends on your goal, as others say. I once met a group of Japanese students iof English that spoke with a pronounced Scotish accent, as their teacher was Scotish. No problem to understanding them. But they would stand out as any Scotsman would in America or anywhere else. I think implied by your question might be another question, If you learn English with one accent, is it then easier to learn a different accent? OR if you practice listening with one accent, does it help with other accents? . From what I've seen one of the main problems with understanding is that people's native vowel sounds are different. These move with accent and region. It seems to sometimes take a long time to be able effortlessly produce a vowel you did not grow up with. Changing it again, to change accent may be challenging, I don't know, sorry. It seems to happen quite naturally for people living in foreign places; they migrate slowly towards the local accent. Sorry, my answer seems to be a definite "maybe".