Yes. When they start cutting rates that would be good time to buy Treasury Notes/Bonds or longer term CDs so you can lock in the interest rate for a period of time.
Expected rate cuts are generally already priced into longer-term bond prices, so trying to get in just before rates go down is basically exactly as hard as market timing.
Higher than 0% yes. Historically rates are still on the low side. And yes they move with the fed rate.