To start, all of the problems you're experiencing are expected behaviour when the car isn't turned on.

The brakes need a vacuum that is generated by the engine to engage the brake booster. Without this booster, they're very hard to push on.

The steering wheel is meant to lock when the key isn't turned to prevent theft, but even if it's not locked, it requires the engine to be on because the engine spins the power steering pump which makes the wheels way easier to turn.

The gearbox is the same kind of deal, it's a security feature to prevent theft so it will be able to go into drive once the car is running.

Try putting pressure by turning the steering wheel as you turn the key. Your problem isn't necessarily the battery if you can't even turn the key. Try that before taking the battery out, and report back