As the title says, I am looking for (a) word(s) expressing something(say a piece of bread slice) is a bit over burned and its outside becomes dark. After looking up dictionaries, I find a few: scorch, char, singe. I am wondering which one(s) are commonly used by native speakers?
(I'm a native American English speaker.) Those words all mean basically what you're looking for but with slightly different connotations.
"Scorch" is probably the most "dramatic" --- if the bread is scorched then it's been so burned that it's basically inedible. You would use this word to emphasize that the bread is burned to an extreme degree.
"Char" is sometimes used to describe this in a culinary context (here's a recipe for charred broccoli: https://whatsgabycooking.com/charred-lemon-broccoli/). "Blackened" is also common here. But food could also be accidentally charred.
"Singe" specifically means to burn only mildly. It can also be used for food.
For meat, we call this "well done", which is the opposite of "rare". There is a continuum of done-ness ranging from rare to well done with "medium rare" and "medium well" in the middle.
For bread, the common word for this process is "toasting". You stick a piece of bread in a toaster to toast it, after which it has become toast.