Broadcom was very light on details about these changes. Here's how I interpret (and these are my opinions -- I am not a Broadcom employee):
1. What part of VMware exactly is included?
a) Workstation Pro is now free for all use cases (commercial, personal, academic). Given the "effective immediately" statement, my best guess is that this applies to the current version - Workstation Pro 17.6.1 - and future versions. Given the mechanisms they put in place for free personal use, they could conceivably allow free use for 17.5.2 and later. But that's not clear.
b) Workstation is no longer available - that happened as of Workstation 17.5.2. Only Workstation Pro. There's really no need for it as Workstation Pro is now free. See 1a)
c) Workstation Player is no longer available. that happened as of Workstation 17.5.2. Only Workstation Pro. There's really no need for it as Workstation Pro is now free. See 1a)
2. What and how do i install and activate VMWare Workstation now in a commercial Environment?
The Broadcom download site has removed "Workstation Pro for Personal Use". I would expect that there would be a revision forthcoming that puts all the legalese in the shrink wrap license to reflect this new policy. In the mean time, I'd take Broadcom at their word that the change is effective immediately. I'd download Workstation Pro and answer the questions during installation like you were using the product for personal use. Given their efforts to "simplify" their product line, I'd be surprised if they implement any kind of license key registration or activation in the product beyond the types of things they already built into the product (a self-installing key) for free personal use.
You would think that they'd release a new version just to clean things up with the new model. But, as normal for Broadcom, no announcement of future plans for release.
3. With what kind of License is VMWare Workstation Pro now licensed?
My guess is that it's still a proprietary, licensed product - not open source or GPL It's just that the license is no-cost.
I'm surprised that the lawyers allowed this to get out without requiring a new version that includes the new licensing terms in the "shrink-wrap" licensing. That's why I'm expecting a new version to be released.