How do I connect an Aluminum "Unibody" Mac mini to a television?

Quite easily. Unlike earlier Mac mini models, which require an adapter to connect to a television, all Aluminum "Unibody" Mac mini models are equipped with an HDMI port and can be connected to a television with a traditional 19-pin "type A" HDMI connector.

Via HDMI, the Aluminum "Unibody" Mac mini models support a television up to 1080p (and the HDMI port supports 1920x1200 on a DVI display with the included HDMI-to-DVI adapter as well). All models also simultaneously support a 2560x1600 display via either the Mini DisplayPort -- for the "Mid-2010" models -- or the "Thunderbolt" port -- for the "Mid-2011" models (Thunderbolt is backwards compatible with Mini DisplayPort).

To adjust the size of the image on an HDTV, the Mac mini models have a revised Displays control panel with an "Underscan" slider option.

Is the Aluminum "Unibody" Mac mini capable of 1080p H.264 HD playback?

Yes. Just like the polycarbonate "Early 2009" Mac mini -- the Mac mini "Core 2 Duo" 2.0 (Early 2009/NVIDIA) -- and "Late 2009" Mac mini models -- the Mac mini "Core 2 Duo" 2.26, "Core 2 Duo" 2.53, and "Core 2 Duo" 2.53 (Server) -- all Aluminum "Unibody" Mac mini models are fully capable of supporting 1080p H.264 HD video playback.

For future reference, note that the minimum officially supported Mac OS X system for H.264 HD playback at "1280x720 (720p) video at 24-30 frames per second" is a Power Macintosh G5/1.8 or an Intel-based Mac with a 1.83 GHz Intel Core Duo or faster processor, at least 256 MB of RAM, and at least a 64 MB video card.

For "1920x1080 (1080p) video at 24 frames per second" H.264 HD playback, Apple recommends a minimum Mac OS X system of a Power Macintosh G5/2.0 DP or an Intel-based Mac with a 2.0 GHz Intel Core Duo or faster processor, at least 512 MB of RAM, and at least a 128 MB video card.

Also see: Which polycarbonate Intel Mac mini models are capable of 720p and 1080p H.264 HD playback?

Does the Aluminum "Unibody" Mac mini have an IR receiver? Does it support a remote?

Yes. Although Apple does not formally mention it in technical details, all Aluminum "Unibody" Mac mini models have an IR receiver and support a remote.

Apple, and third-party resellers like site sponsor PowerMax, sell the matching aluminum Apple remote (MC377LL/A) for US$19. Other remotes can be configured to work as well.