I used a TA last time I went from Smallworld Vacations and...
1) First, like @missoverexcited mentioned, you want to actually do it at LEAST 6 months out. This way you can get first dibs on securing your ADRs. So I would say 7 months at minimum. This will give you enough time to research some of your restaurants and be ready to get your ADRs (which your TA will not get for you). Additionally, you will only need to put down your deposit for all the time up until 2 weeks before you leave, so it's not like you'll be out of a lot of money initially.
2) I would think they can book your flight, but mine did not want to when I went with the explanation "we won't be able to get you as good a deal as you can get on your own." Which is kinda true as airlines are always adjusting their prices and a TAs can't/won't keep looking for the latest price to get you the best deal. So it's actually better if you do it.
3) I found you want to book roughly around the 4-5 month mark from you trip, and then keep watching the rates to see if they go even lower. So for example, if you are going in August, I would say get ready to book around early April or May.