A simple way to check is to use the strings as a straight edge. Fret a string at fret 1 and fret 15 simultaneously. That removes the bridge and nut from the equation, and gives you a perfect straight edge. Then check for a small gap between the string and fret 7. The size of that gap tells you how much relief the neck has. You can change it by adjusting the truss rod. Use very small adjustments (like 1/8 turn) and retune the strings before checking the relief again.

If you need to replace the truss rod nut, there are various techniques to remove the stripped one. Start by removing all string tension (this makes it easier to loosen). For a tool, you just need to find something that grabs enough to get it to turn. A slightly larger allen wrench, a blade screwdriver, a screw extractor, etc. Another option would be to find a bit of metal bar that fits in the socket and super glue it on. Then you can grab the bar with vice grip pliers and turn it.