No hard feelings.
1. Judging from some posts on the subforum, CD version and GOG version are not exactly the same. I don't know how they differ, but GOG often make their own tweaks to ensure the game works on modern systems.
2. I have no idea. Those patches are unofficial and fan-made but they should not be necessary to run the game bought on GOG.
GOG on their part do all the can to assure the game works. If you buy it and it doesn't run well for some reason, contact Support. If they can't help you fix the game, you are eligible for a refund as stated in their Money Back Guarantee Policy.
https://support.gog.com/hc/en-us/articles/115000487189-Money-Back-Guarantee-Policy 3. I can't explain why you have problems with your game. However, you're using a CD version of an older title on a modern system which may or may not have Intel integrated graphics, so it's not surprising something doesn't work. You can try:
-- running the game in a compatibility mode (right-click shortcut or executable -> Properties -> Compatibility tab -> select older version of Windows in Compatibility mode section)
-- this:
http://kingpin.info/?e=619 As for resolution problems. I can't really explain them either, but you're trying to run an older title with 4:3 aspect on a modern widescreen displays. Additionally, your laptop and your TV may have different screen resolutions, and I suspect this may also mess things up. That's why BreOl72 suggested a fan-made patch allowing to set resolutions native to your displays.
In Kingpin subforum I've found links to at least three patches dealing with resolution of this game and other issues. They basically require you to unpack a file or two into main directory of the game and run them. They usually come with instructions in txt files.
http://www.captaindeath.com/kingpin/utilities/multipatch3.aspx http://download.kingpin.info/index.php?dir=kingpin/patches/unofficial/mh%27s_kingpin_patch/
https://www.gog.com/forum/kingpin_life_of_crime/a_small_widescreen_patch Good luck.
Disclaimer: I don't have the game, I'm not using Windows, I've not tried any of mentioned patches, I don't know what I'm doing, does anybody know a way out?