I wonder if there was some type of “cover” that goes on that screw that broke off leaving this one that upper pic I shared. Here’s one I used to have that looks normal. Wondering if that outer piece may have broke off on this one?
Not OK, the former tip of a cheap cast metal Phillips screwdriver is lodged in the slots. It can likely be pried or chiseled out but until then it will be difficult to adjust that truss rod... If it's an item your considering buying then that is IMO a negotiating point for a discount.. Does not appear to me to be a major issue as I have dealt with stuff like this before, but it may require some tools and a vice and some dynamite..
If something isn't broken off in it (and no, you are not supposed to use a Phillips head screwdriver on it), take a large slotted head screwdriver and remove the "nut." Then, poke out the obtrusion from the backside. Then, a little beeswax on the threads and screw it back on. Adjust to taste.
The second pic is more concerning. The truss rod nut is fully backed off. Probably okay with neck under string tension, and not unusual for an older tele... But, no adjustment in one direction, if needed.