Please take a look at the software guide/manual for ADV611: ADV7611 Design Support Files
1) Yes HPA_A-- with no hot plug signal, I'm not sure you could create a working system that is compatible with HDMI/DVI sources. Do you have separate GPIO connected to that signal on the connector? There is a register bit you can set/clear to set the state of the pin in order to pulse it. The source is supposed to read the EDID when it gets this pulse. Without it, probably it won't work consistently.
2) There are registers in the IO map that let you configure which events cause interrupts. You would need to set these up.
3) We have a tool for checking EDID: Advantiv™ EDID Editor With no HPA, not sure if your EDID is being used though.
Dave