^VTHO generated by simply holding the VET on their wallet and OP mentioned that he is holding it in their official SYNC wallet then he should be having enough gas fees I guess.
Yes and also from Masternode.
I don't know did he have enough VTHO to be used for a transaction, but I believe he doesn't enough VTHO to make some trasaction. I thing @OP can buy VTHO and send your VTHO to the address and used them for fee transactions.
I think the rewards will be generated even for simply holding the VET and also different types of rewards available and it will be rewarded to the wallets everyday so he can wait for a day r two or simply buy from exchanges as you said.