1. Just use the beemod instances in hammer, if you are wanting to.
Would love to, but haven't a clue as to how to do so. BEE Mod was removed when I reloaded the original Portal 2 settings in steam. Detailed instructions on where to find these instances and how to implement them would be a great help. All I've been able to find via searches either show you how to reinvent the wheel (create things that are already available in BEE Mod) or how to do simple room designs. As stated before, what is needed is Hammer files with each feature saved by itself as an instance, and some clear instructions on how to implement them.
2. I think you are missing the point. Beemod items were created in hammer. PTI is a bad level editor, and that is for reasons too numerous to list.
Maybe, but creating a complex chamber with standard Portal 2 features is far faster. Item placement is locked into the proper place, and can be far easier to move if need be. No need to zoom into an already hard to see line diagram of the level you're working on, with so many visuals blocking the view. PTI did a few thing right. You can clearly see what is in the level you are working on, and how triggers are connected to items. Also, level shapes can be easily changed whenever you need, with very little hassle.
*3. Just decompile a valve model like a button and use it as a scale reference. *
Once again, you tell me the most complicated way to do things. First, I (as well as other people new to Hammer) wouldn't know where to begin to do this. All I needed to know was a number to assign to a common element in Portal. I actually found this in some comment under a YouTube video. FYI for other people with this question, a standard room building block in the PTI is 128 Blender Units. With this information, I now have a rough scale to work from. I even found a YouTube video that had a link to a scaled human character that can be loaded in Blender.
In closing, yes I can clearly see that Hammer has far more flexibility, but it is at a cost of usability. Not everyone has the time or the aptitude for working in an environment like Hammer. That doesn't mean that they can't have good, creative ideas that can be implemented with the PTI, and even more so with BEE Mod.
Using PTI and only a few BEE Mod items, I was able to create a chamber that requires the player to actually be able to convert numbers into binary in order to solve the puzzle. I'm sure not many Portal 2 creators, even those using Hammer, have thought to do this. And I've played many user levels that were challenging and creative that only used PTI. And I've played levels obviously created with Hammer with very little challenge to them, and had nothing of interest except some eye candy. So please, try to avoid looking down your nose at people who rely on PTI. Technical know how and creativity are not always linked.