xbox one starts up in 640x480 and when i change it to 1080p it changes but the screen is green ...

I can change the resolution out of 640x480 but if I choose 720p, 1440p or 1080p the green screen start again.

I tried using another device (laptop, xbox 360) with the same HDMI cable and they are displayed in 1080p perfectly. As soon as I reconnect the HDMI cable on my xbox one the screen shrinks in 640x480

I also had this problem, I found that my tv runs 720 to 1080p. When I switched the settings and reset the resolution it changed my Xbox display settings to 640x480 which my tv didn't support. To change the settings I had to use an older tv that supported
640x480 and changed it back to 1080p. Placed the hdmi into my tv and it was running as normal

This evening, I turned on the Xbox. The TV was working in the main tile. I signed in to my wife's profile (not Xbox Gold), opened Skype and set her up so she'd be signed in when I try to Skype her, and then went back to the Home screen. The sound was working,
but I had the No Signal Detected message when I started TV.

I signed her out and signed in as me and the problem persisted.

I started poking around in settings and changed the source type from Auto-Detect to HDMI. The screen resized to 640x480 and it did not scale to fit my display. I went back into settings and changed it back to 1080p and then went back to the Home screen.
I started the TV app and it was working.

I will have to wait to see if it happens again, but it makes sense that it's the Auto-detect feature that is causing the problem.

As you suggest, while my console and television were turned off, I plugged the HDMi cable to another port on my tv.

But still the same problem, when I want to change the image quality other than 640x480, it start freezing whith a green halo

If you switch your TV connection settings in the Xbox One settings from "Auto-detect" to HDMI or DVI it will display the only resolutions the Xbox One is capable of even if your TV doesn't support some of those resolutions. You can set it to 1080p, but
if your TV doesn't support it the screen will go black. If you set it to 1080p and your screen didn't go black then your TV accepts 1080p, but your TV might scale it to 720p.

Unfortunately, many TVs don't accept either 1080p or 720p, so without 1080i output the Xbox One is forced into standard definition 640x480, which by Microsoft's own admission is not recommended. 640x480 resolution on a system meant to display in HD looks
terrible and it makes the Xbox One look worse than the Xbox 360. Many of the Xbox One's main features do not even work in 640x480 like the big app tile goes to a black screen and when snapping apps the left screen goes black. Not to mention that any on-screen
text is illegible and the system is letterboxed even on a widescreen TV because 640x480 is a 4:3 resolution.

Microsoft could easily fix this by adding 1080i output in an update, but they have been ignoring this, even though it is one of the biggest requests on their new feedback site.