Is it ok to use a frame hardboard siding as a tennis wall

I would suggest using composite or PVC lumber in this application. Composite boards are moisture and rot proof. They are made with wood fibers and recycled plastics. Most are paintable so you can match colors. The other choice is PVC boards. Some are paintable, but most should be used in the factory color. If you do paint PVC, use a product that is specifically for plastics, regular latex paints will not adhere properly.

Pressure treated lumber is a good product for this application, however it is difficult to paint. It usually has a high moisture content and must be very dry before attempting to prime and paint. Not a good base for paints, however better for stains.

I'd stick to composites in your situation.

I'm a little lost. First, what are you using to attach the furring strips to the concrete? I'm hoping some construction adhesive and a few concrete screws/anchors to bear the weight You could use the same thing to attach the Hardee-board directly to the concrete (with a layer of moisture barrier separating them to keep moisture from the concrete seeping into the siding). I'm also not sure why you're telling us what the garage door is framed with if these 2x6s aren't a substantial part of the anchor for the furring strips.

Anyway, assuming it cannot be done any other way, I'd say that using 1" nails where 1-1/4" is recommended is acceptable; maybe use a few more along each furring strip to compensate for the decreased "bite" of the shorter length of each nail. Understand that a pneumatic nailer will drive the nails down beneath the surface of the Hardee-board, so even with 1/16" clearance that 1" nail may contact the concrete. The only additional recommendation I would give is to nail in at a slight downward angle where possible, as if you were hanging a picture. The angle will not only give you a little extra depth to drive the nail, but the angle will increase the leverage the nail has to hold the siding, like using a nail to hang a picture.