It uses a mini/micro? USB (one of those small USB ports for power). My device came with an adapter that I could attach to my TV's USB port, so there are no dangling wires. If your TV doesn't have a USB port, you can just connect it to a normal power outlet (it's the same adapter as for many other Android devices)

How long does it take to boot? ie from power being applied through to it showing up as a target in other devices/apps.

(The reason for asking is whether you need to connect it to a full time powered port, or one that only comes on once the TV etc are on. If it takes 5 minutes before becoming visible that would be problematic but 5 seconds would be fine.)

The HDMI connection provides 5V power.

I believe that is only true for MHL HDMI. They likely use USB power so that it can be used on any HDMI port, not just MHL-enabled ports.

HDMI does provide power [0], but a very small amount (elsewhere on this thread someone said 50mA). MHL provides more.

[0] http://www.hdmi.org/installers/insidehdmicable.aspx

I don't know what MHL HDMI is. How do I verify if I have one? My TV is 2009 Sony Bravia and it transmits audio (since I can use Apple TV).

I would guess that you don't have it. The Roku Streaming Stick uses MHL and it only lists a handful of compatible TVs. http://www.roku.com/streamingstick#roku-ready