Sheever literally laughs at the end of your clip and they are still talking about suicide. I don't know why you keep thinking its a big deal for her when she's laughing right there. Seriously just watch it again, its not even right after the clip or something like that its included in it.

Bad taste or a poor joke does not mean everyone should get offended. The issue with taking offense to literally everything that could possibly be interpreted as offensive in any way is you delegitimize any actual complaints. Its the entire premise of the "Boy Who Cried Wolf" childrens story and all its variations. Your first point for example makes it harder to take your second one seriously because while the second one is at least somewhat valid on its own (it didn't really add anything to the cast and was just a stupid comment) the fact that you say it in the same post as such an absurdist complaint with your first one makes it impossible to take seriously. Or, (and this might be before your time, idk) there was a point in time where people were posting threads on reddit every day about how unprofessional players were in pubs and calling for bans or punishments for them flaming people. Meanwhile Tobi got away with this classic and nothing came of it apart from a casual tweet because they were too used to all complaints about behavior being really stupid shit like complaining about players for flaming.

Chinese BKB's is fair since you may not have been around when that joke was going around. Considering NA dota jokes happen all the time though and even in this event its a little disingenuous to harp on something that happens when Slacks does it and then completely ignore something that happened in the same event.

Regarding outrageous implications you've made:

First one is literally there to bully and make fun of everyone interested in the tourney.

Second one was clearly not something a professional host should be saying in front of thousands of people

I saw no acknowledgement of this either on Slack's twitter nor PGL nor reddit.

However yesterday he was once again on the 1v1 and again doing things that can be considered bullying co-hosts and viewers.

All these are talking about how Slacks is a bully for making a joke about how he's bad at the game. You also directly imply not only that he should have changed his behavior with the last comment but also that a formal apology should have been made because he made a joke about how bad he is at understanding and playing Dota with the third comment I quoted here.

Correct me if I'm wrong but what could this possibly mean:

I saw no acknowledgement of this either on Slack's twitter nor PGL nor reddit.

Other than wanting a public statement being made about how its not ok for Slacks to make jokes about how he doesn't understand the game?

Compare this to what James said at the Shanghai Major. What's worse?

Ah yes, the man who in the first couple minutes of the cast talked about jacking off to handicapped porn the night before and called professional players bottom bitches. Part of the problem with James if you read his post was that he also didn't listen to Perfect World - there's even a part on the panel where he says he's being told to cut to break but is refusing to and tells the panelists to keep talking. Honestly I don't think James should have been fired but to compare him to Slacks is just absurd, it really just looks more and more like you have some vendetta against Slacks because the two aren't even close to being comparable. This is what makes it so hard to take your post seriously - should slacks have made a suicide reference? Probably not, it really didn't add anything of value. Is it bad enough to the point where we can compare it to James at Shanghai, call for a public apology to be made, imply that Slacks should get the same treatment as James and get blacklisted, and try and shame PGL for it? Absolutely not, not even close. Its ridiculous that we even have to have this conversation which is why you are getting so many "trolls" I don't even know why I'm taking the time to answer this seriously tbh.

Does PGL condone these words coming out of one of your hosts?

This is also the epitome of overreacting to a mundane comment about suicide. In a game that has suicide in it as a mechanic of all things.