I really don't know but some brief checking online indicates pets are not allowed on trains.

Only if it is an assistance dog, such as a guide dog for visually impaired people. Otherwise animals are not allowed on public transport.

Yes, free. Parking is limited and you have to pay. You can jump on the train and get off at Roma Street station then you have a short walk to the Parklands. Cafe is expensive and not worth it, so take your own....cheaper and nicer to have your own picnic.

Yes on a lead

Parking is available in a few places around the Parkland and within Roma Street Parkland. And YES there are disabled parking spaces within the parkland.

I would say it is a few minutes walk. I also seem to think there is a ramp. Not absolutely certain.

Parking varies on different days. If you train it to Roma Street is is not a far walk from the station. The parking can be on the streets around the grounds at meter parking or in the parklands.

There are five meeting points but the information centre is the most common one. It is located above the enormous waterfall.

visitbrisbane website tells me "Parking is available at a number of locations throughout and adjacent to the parkland. There are nearly 200 car parking spaces (including 11 disabled car parking bays) within Roma Street Parkland. Car parking spaces are located at College Close Car Park and along Parkland Boulevard. Undercover car parking is also available within the residential apartments complex. Parking fees vary during the week and weekend."

None that I saw. And actually, I haven't seen any b-ball courts within probably 3-mile radius of Roma Street Parkland.