Is there a way to keep the operator from leaving the main screen on the run tab? Such as locking the i/o tab, move tab, and the log tab? I found that you can put a lock on the program tab so that will require a password to access, but on the run screen you have access to a couple tabs that I don't think we want our operators messing with if we can prevent it.

Not that I'm aware of. If the robot crashes do they reset the cell or do you have someone else who does that?  That's what you need access to those screens for, opening or closing grippers, moving the arm, etc

That is what we can't quite decide on. We have gone back and forth about whether or not we want an operator to recover from that situation or if we want a specific person that has more training with the UR to do it. How do you handle the situation of a crash?

We have trained the operators to handle that situation. Only when they do not know what to do with a specific issue do they escalate to a more trained person. Our objective is to keep the robot running as much as possible whether with our current customers or when they were our own robots. 

When we had robots in production we would provide training to the operators that were tasked with front line running the robots, we treated them as our first line of defense so they knew how to recover them pretty well. When something occurred that was not normal and they did not know what to do they could escalate to a robot technician who could then escalate as well to a manufacturing engineer. 

Today most of our programs are "auto" recovering in that the operators don't really have to think too much about how to get it restarted, the robots for the most part know how to get themselves back to the start of the program. A number of our programs can be restarted from various points within the program making it even easier for the operator. We focus on making it as easy as possible but still provide training. 

I would also recommend to train the operators to handle that kind of situation. When I was working in a big company with almost 100 robots, I had two kind of sectors.
First had people trained to do a recovery manipulation, so the operators were able to run easily their machines even in case of default.
Second had people who didn't understand robots and they didn't want to understand how it works because they weren't trained for it. So when then machine wasn't working, it was always the fault of the robot. And I would say that 90% of the time, it was a sensor or another actuator fault that they should be able to fix.
So training at least a minimum operators save time and involve them, they feel more responsible. But of course the recovery method as to be as simple as possible.