Someone please correct me if I'm wrong. But:
1. HDMI adapter requires Honeycomb 3.1, so you would need to run custom rom.
2. Not sure if adapter will fit in as tablet it's few millimetres thicker.
3. As per point 1. Requires 3.1 Honeycomb, so again need custom ROM (something to do with HID devices over bluetooth, if you google it you should be able to find some more info.
Samsung Galaxy Nexus
Samsung Galaxy Tab 10.1v
Rom:Rs HDBlogICS TEST v0.5.1
Rom:TAI v5 Manila 2D