The ADV7612-7511 is only ~$200 can can be found here. http://ez.analog.com/docs/DOC-1713
It also comes with scripts and AVES which allows full access to all the devices http://ez.analog.com/docs/DOC-1789.
1) Just do it like the evaluation schematic and you will have access to all the registers. We have scripts that write EDID to the 7612
2) Yes, it looks like a regular I2C device
3) Yes, initialize the part then write the EDID block. It should then work fine.
4) digital data lines and clocks are 3.3V compliant.
Since this is for a thesis I'd strongly suggest you purchase the low cost board linked above, it comes fully functional, with driver software, PC interface software and scripts. You'll save more time/money then trying to build your own board which is not easy when dealing with 1080p
If you have any other questions please ask.