A little play isn’t a big deal. Does it have play even with the hubs tightened down? You should tighten them down to snug and then back off like 1/4 - 1/2 a turn to allow them to spin freely.
“Overcentering” is what I’m assuming you’re referring to as the Ackermann effect causing the outer wheel to steer out slightly at max steering lock. This is normal and how it’s supposed to function. There is no lock or stop on the steering normally, the steering stop is when the tie rods hit the steering shaft.
Frame protectors usually come in a generic model that fits most karts. KartLift made some good ones, or J3 I believe sells them as well.
Good idea to keep spare grub screws on hand, as sometimes they can work themselves loose and fall out if you aren’t checking them occasionally.
For lube, Tri-Flow or similar for daily bearing lube and Xeramic, Bel-Ray, or something thicker and more durable for the chain.
turns out the shop that was handling the kart (when putting it back to original stock for owner), misaligned the spindle/hub spacer and deforrmed it causing the play. bearings are good in the front, i need to work my way to the back.