Yes, it's the ferry that ends in Parramatta. I don't think the ferries have particular names.
If it's a nice day, certainly sit outside - you might need sunscreen, hat, water etc if it's really warm or a mac, fleece and umbrella if it's a bit cooler as happened to us the last time! (only we didn't have any of them and had to resort to sitting inside)!
At Parramatta, you will need to leave the ferry walk the short loop ashore and reboard.
Highly recommend getting an Opal card and loading with sufficient funds for your trip - week runs from Monday to Sunday and the day costs are capped. You can get a refund on the card but it lasts 9 years before they cancel it, so hang on if you think you will go to Sydney again. This will be our third visit and we can't wait.