Video Quality choices and ability to turn xbox on from app

I would be trying your Xbox on another LCD HDTV to see what quality difference there is. As it may be your TV's ability to show component connections compared to HDMI connections.

Have you looked at these settings mentioned in the below link?

support.xbox.com/.../improve-video-quality

Are you asking how to change settings to use less data? With youtube you can lower the quality of the video. This can virtually be done from any YouTube app. On your xbox when watching a video you can change resolution from the more option and choose a
lower quality. Should be similar from any other youtube app on other devices. The more option on you xbox app will be the three ellipses.

I did find this tutorial on how to change it on your smart phone, and it may transfer over to your console:

1. Launch the Prime Video app in your smartphone.
2. Tap on the menu icon and select Settings from the menu.
3. On the Amazon Video Settings screen tap on Stream & Download option.
4. On the Stream & Download screen, you can tap on Streaming Quality and
   Download Quality to change the respective video qualities.
5. You can choose the video quality from data saver, good, better, best or the highest quality possible.

Other than that, it may not be possible to lower the quality as I assume the Xbox one Amazon prime video app assumes you're on a non-metered connection and doesn't see any reason to lower your quality.

You could contact Amazon support if you can't find any option or if that doesn't work, above.

I was just coming here to post about the Amazon Video app. Just started using it recently and noticed that the video quality sucks. Is this how it always is with this app? No HD quality like the Netflix app?

I love the app too. The UI is really nice and the video quality is great. I like that you can pair smartphones/tablets to it so if you're watching a video on your phone/tablet, you can tap a button and have it play on your TV via the Xbox One - kinda like
the Chromecast. The only update I want to see is the ability to share Game DVR clips direct to YouTube, although that's not really related to the YouTube app itself.