I have a technical question on how SegWit works:
With current transactions, the number of confirmations acts as a guarantee of the Bitcoins deposited. Many services require between 3-6 confirmations to show that funds have been deposited.
With SegWit, does this logic still remain?
I may be confused with what SegWit and Lightning does. I've heard some mention that it can give an instantaneous guarantee of fund transfer, however I don't see how this would work without confirmations of the original transaction...
You're confusing Segwit with Lightning. Segwit does not touch confirmations or anything like that, it only affects the data itself. The number of confirmations required will still be the same.
Lightning is different and allows instantaneous transactions because the transactions actually happen off chain. The guarantee that your transactions are final are done through incentives and retaliation. The only onchain parts of lightning are the opening and closing of payment channels.