For peace of mind and sanity, you'll want to fence off your nicely planted areas while you're working on training.
You can use T-stakes from a farm supply store with soft temporary fencing (nicknamed "snow fence", sold in rolls).
Put a "door saver" protector over the screen door.
Those will help you manage your puppy, while you work on training, and will prevent further squished plants and torn screens.
You can start working on two commands right away:
"OFF" (no paws on doors, no paws on fences, no paws on gates).
and more importantly, "WAIT". My dogs can't go through a door or gate until I say "Okay". This prevents door dashing, since the dog automatically stops and waits in front of a door or gate. If the puppy is bouncing around, nosing the door or scratching, too bad, you stand there and nothing happens until the puppy yields and waits. Make the puppy "Wait" before coming inside, and also make the puppy "Wait" before going outside.
You have to be consistent, but it works. 9 months is old enough to be waiting at every door, gate, or opening.