Can "whether" be used in a question that starts with "Are you sure..."?

No, it is not correct. "Whether" is not used in this way. If you are trying to ask someone to decide between an apple and an orange, the correct way to do so is as follows:

Would you prefer an apple or an orange?

"Whether" is used when referring to a question indirectly. In informal speech, it can be often replaced with "if". The following are all correct ways to use the word "whether":

I asked him whether he wanted an apple.

I asked him if he wanted an apple.

I asked him whether he was sure he wanted an apple.

I asked him whether he preferred an apple or an orange.

Do you remember whether it rained last week?

Do you remember if it rained last week?

For more information on the use of "whether", see: https://dictionary.cambridge.org/us/grammar/british-grammar/if-or-whether