Yes, all interactions with the platform will require a small amount of SOL for the gas fees on the blockchain.
Yes. The Solana blockchain requires a small amount of SOL to store the state of your positions on Drift. This costs 0.035 SOL. This is called Rent. This fee is only paid on the creation of a new account and each subaccount.
Note: To trade on Drift, you'll eventually need more than 0.035 SOL to facilitate and approve transactions.
Yes. If at any time you decide to close your account you will get the rent back for that associated account.