2. Tereré is a cold preparation of yerba leaves. It's prepared very similarly to mate, but with ice water. Paraguayans still call it mate when it's hot. Argentinians from the fart north also drink tereré and sometimes even use cold juice or soda in place of the ice water.
3. Paraguayans drink mate any time in the winter, but in summer it's typically only early in the morning or late at night. Tereré is way more common any other time of day in summer.
rooibos is a different plant, and herbs obviously are, in every day speech (a lot of) people call them tea, but technically they arent. They are infusions used in the same way as tea, but with different plants. If it is not made of tea(leaves) it isnt really tea. (but it is easy to call em that, I usually do aswell, though I know the distinction, "do you want an herbal infusion?" sounds kinda I dont know what, but you are bound to get some funny looks ;) )