Your TV has a upscaler built into it and unless your going with a multiple hundred dollar solution like a retro tink the build in one will be better then almost any upscaler you find on amazon. Your best bet is to get the best signal out of your xbox possible for the TV to upscale.
The best HDMI adapter will be the one Chimeric makes but they are hard to get and expensive if your looking for a cheap option I would go with a Hyperkin or a Pound Adapter.
Those all take the component signal from the Xbox and convert it to HDMI.
The other option if your not afraid of semi dificult soldering is to get a MakeMHz HDMIadapter. those take the digital signal from the motherboard and convert to hdmi.
No, those cables are only for composite video and stereo audio, and will only carry a 480i signal.
You need something like a component to HDMI converter box, or one of the Xbox to HDMI cables, like those sold by Pound and Chimeric Systems. The latter is the best option without modding the hardware, but has a long wait list.
Yeah check it out: https://www.amazon.com/dp/B07D19QQHW
"after modding it again if necessary, I can run NTSC games on it, and also enable 480p and 720p on the dashboard?"
How is it modded Soft-mod or Hard-mod? You can change the zone from Pal to NTSC on any version of Xbox and enjoy the HD mode with 480p, 720p
"Since I don't have a CRT, and the component cables seem to be too expensive, what is the best HDMI cable/converter (for maximum image and color quality)? https://www.amazon.com/POUND-Link-Cable-Original-System-microsoft/dp/B07D19QQHW this one seems to have positive reviews, would you recommend it or is there any better solution?"
Do not even think about using the pound POS (Piece Of Ship) cable and in my view there should be a law against setting crap like that.
You can join the list of people wanting HDMI converter from Chimeric Systems or have a look at this one there is a small issue that it will not work on a version 1.0 but all other versions are all good.
https://electron-shepherd.com/xbox2hdmi/
Here is a video