I personally would never say
нареза́ть in any of your examples (when it is used in the questions). To me it doesn't sound natural. I'd use
наре́зать in both questions and both of these questions sound like a polite request to me, rather than a question.
Actually, I just read the Quassnoi answer to the very end and example given at the end shows good use of
нареза́ть form in questions. I just interpreted both of your questions as requests originally and didn't think about other possibilities.
I can say
Можете нареза́ть хлеб.
Note, that it is not a question, but a statement.
In the sense of giving directions/permission: You are free to go and slice the bread.
Можете начинать нареза́ть хлеб.
You are free to go and start slicing the bread.
While it is not so clear with the
нарезать form of the verb (present tense), there is a clear difference in the meaning that depends on the stress when this verb is used in the past tense. Russian language has just one past tense, unlike English, but you still can express subtleties.
Я наре́зал хлеб.
This position of the stress in this word means that the action has finished. Either just finished (present perfect (?)) or simple past tense. It can be translated as: I have sliced the bread. I have finished slicing the bread. I sliced the bread (yesterday).
Compare it with:
Я нареза́л хлеб, когда произошло что-то.
Past continuous (?). I was slicing the bread when something happened.
Я нареза́л хлеб в течении пяти лет (работая там).
Present perfect continuous (?). I have been slicing bread for five years (while working there).
нареза́л form in some sense implies continuous tense.
Not sure if I labelled English tenses above correctly.