Is it possible to play games from my HTC Desire HD on my HD-TV? Is it possible to play my 3d games on my HTC Desire HD and mirror the display to my HD TV?

I have a Sony Bravia 55HX820 3D LED TV with 240 Hz, which was top of the range when it came out in 2011. I don't think it has MHL technology but I know there are adapters so I can connect via MHL. Neither can I find anything that says my HTC Desire HD is MHL compatible as I don't think it is.

I can stream videos photos, music etc to my TV wirelessly via DLNA -- but does anyone know a way to play my games from my HTC DHD to my HD TV via HDMI? The phone doesn't support MHL mirror image to TV. I have a lot of high quality games on my phone.

Moreover: What would the quality be like -- as the phone screen resolution only is 400x800 -- but display in 1080p or even 720p on my TV mirroring my phones image.

My phone isnt rooted. I'm running Gingerbread 2.3.5. I'm thinking about rooting my phone and updating to Android JellyBean Rom. Does anyone know a possible way to do that without to much quality loss on the TV -- as it looks good on the phone but the phones resolution on my 55 inch tv would look horrible! Also, would updating to JellyBean make any difference?
Taking a look at the device specifications reveals:


The Sony Bravia KDL-55HX820 gives you four HDMI ports at your disposal according to TelevisionInfo.Com
The DHD doesn't have video out capability according to HTCDesireHDForum


So while your TV would support it, your DHD won't. Updating your device to any other Android version won't change that: the hardware does not support it (the DHD has no HDMI port, and its USB port is not MHL capable according to the information I found).

With that pre-condition broken, all the other questions are rendered meaningless. But for curiousity: Even if your Android device's screen can only display 400x800 resolution, the HDMI signal should carry the source resolution (and not the screen resolution). So if you e.g. try displaying 720p, it would be "rendered down" to 400x800 for your device's display, but if the HDMI connected device supports it fully, it would not be rendered down on the other end, to my understanding.