1. Is the left eating itself?
I think this depends on (as mentioned in the video) whether or not you consider what we call "the left" to actually be liberal in the classical sense. I'll let that point go for the sake of brevity. Also there is a separate debate for what should be allowed on a college campus rather than society as a whole since there are certain considerations with regard to academic standards for speakers in university that do not apply elsewhere. I'll skip that point as well for the sake of time.
The problem with the far left is twofold:
First, that people actually seem to be vying for the title of "extremist" and that creates a competition that is actually a race to the bottom. If a radical feminist declares all men rapists then any others who cherish the title of "radical" have to go at least that far to get the title. Then that is your new baseline for conduct- meaning that if you want to be radical after most feminists have made that step you must go even further. Normally this story of exponentially increasing madness would end with ridicule and public opinion destroying the extremists whether they are on the far left or the far right but the crucial difference in this age is that both sides have carved out "safe spaces" and are becoming totally insulated from reality.
Second, the left has an additional fuel for the fire of craziness in that they control the culture so completely that their brand of crazy is protected. If someone on the right or even fellow liberals question the quantum leaps in belligerence or the faulty logic that so often characterizes extremism, they can be destroyed by the far left. You can wreck a person's career or even their life for disagreeing with your ideology, ignoring any greys in your black and white conclusions about them. Indeed even if a person is totally wrong, and I can think of many on the right who are, it reflects poorly on us as a society that we might silence them with a sort of mob mentality. The theoretical from the discussion in the video "would you invite a Nazi to speak to an American college in the 1930s" no- I wouldn't, but I wouldn't support barring them from speaking either. If they're wrong then just hearing their ideas does not damage me. If you begin censoring terrible people and terrible ideas you allow the scenario that someday in the future, in addition to the moral implications, that you might be eaten alive by the censorship beast that you created. Principles aren't principles when they benefit you only, they are only principles if you apply them equally in situations where it is inconvenient for you to do so.
Standards on the left have gotten so high that few on this Earth could ever live up to them. Not one person could be politically correct all the time and have anything interesting to say. Not one person fits perfectly into all the competing categories on the left that is nominally a coalition of disenfranchised people but in reality is increasingly becoming a checklist- because if you disagree with 1% of liberal ideology and you frustrate the cause you might be disposed of (depending on several pragmatic considerations and certain political/social circumstances) as a heretic. A similar situation has developed on the right, and I don't think I need to work to hard to prove that. The wave of immense pressure that the right will exert on a conservative that renounces Trump is self-evident. I believe it was Ted Cruise who called Trump cancer and then flopped to asking to be his running mate-
Trump/Cruise 2016, "I'm with cancer" has a nice ring to it doesn't it?