Book your ferry ticket on the Tallink ferry online before you go, they have the newest ship, and it's very kid-friendly. Tickets can be changed for a small fee if you need to come back earlier or later.
Estonia is very far north, so it can be cold! Summers are typically cool, not hot.
Take the earliest ferry from Helsinki to Tallinn - The earliest ferry leaves at 7:30 am. If that is too early, you can also take the 10:30 am ferry and still have plenty of time in town.
All seasons are great, but if you visit in winter, expect snow! Summer is mild, a light jacket/sweater will likely be needed.
Book ferry tickets as far in advance as possible. You can change the times if needed for a small fee, but the best deals tend to be with advance reservations.