Never had either happen, but
Trigger guard/housing first. When you close the trigger guard, does it get tight/hard to push to lock about 3/4" to 1" before it reaches fully closed? It should. That means there is the right amount of metal (in the right spots) and the right amount of distance (wood) between the receiver and the trigger housing. Also, look at the pins on the trigger guard? They can be worn (flat spots that are visible) and it won't lock up right. Replacing the trigger guard may fix it if the pins are worn. If not a worn pin issue (compressed stock/wood) that could be fixed with small amounts of epoxy placed in the right spot under the trigger housing (you'd have to see/read up on that one - I remember our M14 stocks being done that way, but I've never had to do it on one of my rifles).
Operating rod popping out? If you've replaced the operating rod are you sure the one you bought was in spec? If it was then it may be a worn receiver rail. I'm not sure how often rails are the problem (never heard of it). There are folks who rebuild operating rods. If you can find someone who does that, and your receiver rails are the issue, you could have them build up the tab on your operating rod a little larger than usual so it would "fit" your receiver better.