Can there be a swap with zero notional on one leg alone? If so, what is the swap used for ?
While mathematically anything is possible, it does not make any sense to have a swap with zero notional, as it no longer is a swap.
For fixed for float interest rate swaps, if the swap rate is zero, while notional is not, that would mathematically be equivalent to a zero notional on that leg, since the whole leg is killed. Killing the fixed leg equals a series of FRAs; killing the floating leg equals a stream of zero coupon bonds. However, for sinle ccy IRS, the notional is shared among the two legs.
For a cross currency swap, if one of the states that issues the currency got totally destroyed, meaning that the exchange rate for the notional went to zero, then sure.