You could check the specs, Ohms, requirements for the oil pressure sending unit, it may be failing. If that's not it, then check the gauge. Gauges can easily be verified by getting an affordable aftermarket gauge and installing it. Also check the sending unit wire, it pass by some hot items and could give a bad reading if shorting out. If the pressure returns to what you expect, then you've found the problem. Beyond the gauge components, you're into changing the pump, which isn't too bad of a task, just dirty.
As for hard starting when hot, you need to understand the differences in circuits used, both electrical and vacuum, of cold verses hot. When cold, your distributor gets vacuum advance then turns off once it warms up. On California CJs, you only get distributor vacuum advance in high gear, otherwise it's off. So, a bad vacuum hose on the warm cycle could be a contributor, but not as likely as an ignition issue.
An ignition coil will always run great when cold until it out right fails. As the coil gets warmer, the spark gets smaller and you'll have issues with it starting and running. Pull the coil wire off the distributor and clamp it about 1/2" away from any metal on your engine and turn the key. You should see a big fat spark. If it's hardly noticeable, change it out, they run about $12 and up. Any standard coil will due for testing.
I've also suffered an issue with a vacuum leak under the carburetor that only appeared when the engine was warm. You can spray carb cleaner around the base of the carburetor when the engine is running. If you the idle changes at all, you have a leak. Keep a fire extinguisher, wet towel or garden hose handy in case there's a fire from the spray. In my case, the base of the carb was warped.
All these engines need is gas, air and spark to run. Air is usually a given, so the last thing is gas. Usually it's a pump issue. The mechanical pumps allow vapor lock which occurs when the engine is hot. Install an inline electric pump with a pressure regulator and return line and vapor lock will never happen again. If you have vapor lock, you shouldn't smell flooding from the carb. Pull the aircleaner off and have someone turn the engine over while you watch for fuel to spray into the carb. First look at it when cold and compare when it's hot. Should be the same.