Welcome, RomiSi 
The local equivalent of butchers/ poulterers/ fishmongers/ greengrocers/ fruiterers/ bulk food suppliers is the "wet market" - theyre in just about every district. The smell can be dire, but turnover of stock is so high that you're not going to go down with a lurgy from buying your meat or fish there.
Note however that local people do not use the same cuts of meat or many of the same species of fish as wherever you might have come from ... if you want a properly cut rump steak, haddock or the like, you DO need to go to an expensive, western-style supermarket (same as you need to find a specialist oriental products shop if you want to get something like dried scallops or chickens' feet in a European city).
And of course the stallholders are doing those jobs mostly because they do not have the education to get easier or better paid jobs (many of the older ones might not have been to school at all), so don't expect much in the way of English.