Reddit mentions of USB Type C to HDMI Adapter 4K - Newforshop USB 3.1 Type C Multiport HDMI Converter for MacBook, Chromebook Pixel Devices and More USB C Devices to HDTV/Projector

I've got the silver, with the 8th gen I7, 16 gb, and 512 ssd. This is the 1080p version. As for your questions.
2: No, I think spec for the usb C port is fairly typical, they're thunderbolt usb C ports so anything that's compatible with those ports should work fine for you. The problem, I think, comes in with these cheap adapters. If you read the reviews for the cheap adapters (https://www.amazon.com/USB-Type-HDMI-Adapter-Newforshop/dp/B075M1TB97/ref=sr_1_5?s=electronics&ie=UTF8&qid=1511140901&sr=1-5&keywords=usb+c+hdmi) this is a common concern. They work 75% of the time, and for their cost it's worth it. As for my problem with the external hdd, this is also a common complaint with these cheaper adapters. Apparently when using these adapters and an external hdd, the adapter gets hot. So that being said, the adapter I referenced above, is fine for me; it works, I use it for HDMI and a usb 3.0 thumb drive.
3: As for the sound, yes that bothers me too. I'm not going to return my unit, because I do feel that it's a software problem. The fact that it addresses itself when I restart the PC tells me it's a software issue. But that being said, I haven't had the issue in about a week or so of typical use. In a month of use, I've had the crackling sound (during unplugging or plugging usb drives) happen 2-4 times. Each time, I restarted the PC and it went away. HP updated software/bios about 4 days ago with the bios updated targeting audio; hopefully that addressed the issue. I haven't had the problem since the update.
4: I did not get the new pen. I was unaware of a new pen. I got the pen with the two buttons. It works really well. Being the first OEM stylus I've ever used, I really enjoy it and it seems responsive. Additionally, MS software seems fairly optimized for it. My unit, purchased at Bestbuy also came with a pleather sleeve with a handy pen holder too. Very pleased with the package.
5: The keyboard is solid. I can't imagine complaining about the side home, etc buttons. Honestly I didn't even notice that they're side buttons. My old Acer aspire s7 had those buttons tied to Fn + directional buttons, so nothing really bothers me about this keyboard setup. Maybe if you're tying some macros to them or playing games it's a problem, otherwise there's no problem with this setup.
6: I would assume that most current PC games turned all the way down for graphical fidelity should run on this PC, but I'm the wrong person to ask. Since this uses an Intel graphics chip, I assume you could only get away with games turned down.