Hi Twinklette - welcome to the H side. I got a 1959 Kelly 28 a few months back, rigid as the one you've pictured. I would love to use it everyday, but she's a bit on the delicate side and find dealing with the straps/flap a bit of a pain when I just need to get in and out to pay for groceries! That said, I love the look and wear her with everything from dressy outfits to very casual.
Re: authentication - there should be a date code but it may be very hard to see after this many years. The zipper pull on the inside doesn't look like original H to my untrained eye but many it's been replaced?
Re: strap, H will make a strap but it may be hard to match the leather exactly. I know some may think this is sacrilege, but I just got a black leather strap from eBay for $12!
There are tons of modelling pics on the Kelly clubhouse thread and the size reference thread to help you! Best wishes!