I think in situation #1, it would be a non-issue, as long as you keep your cool. If anything, I believe it would ensure that the dingbat would not get angry and attack you out of road rage. The dingbat's perception of the incident may be different than yours (i.e. you hit him). On a side note, if they are changing their nails, I would be suspicious they were an alien.
Situation#2 seems to show malicious intent on the part of her, which could get her into trouble. I think indeed you would be at least be detained and questioned. Next, you would both be separated, surrounded by several cars with flashing lights, along with the inevitable rubberneckers
It would be your word against hers, and she would likely be pressured by LEO into 1) making a statement against you, or 2) admitting she lied. I think the question would eventually be asked, if you actually pointed it at her. Speeding to get away from someone that is in "possession" of a gun legally is not a legitimate reason for speeding. Any LEO should know that, and try to determine if a threat was made against her.
If she told you this in passing as a joke, she should be aware that the tables could turn on her, and she would be in serious hot water, with possible jail time. The court system takes such false claims seriously in my understanding.
This is why it's best not to let anyone you know at work that you open carry, or even have a gun, IMHO. They may not like you personally, or for some political reason.