They are compatible if the desktop board BIOS contains support for the processor you are installing in your system. Prior to purchasing your processor, it is a great idea to check with your desktop board manufacturer to see if your processor is supported on their board.
No. The Intel® Core™ i7-39xx/i7-49xx Processors Extreme Edition use the LGA2011 socket and the Intel® Core™ i7-5960X Processor Extreme Edition uses the LGA2011-v3 socket. Each socket is keyed differently and has different electrical and mechanical requirements.
Intel recommends using memory that adheres to the Jedec memory specification for DDR3 memory which is 1.5 volts, plus or minus 5%. For DDR4 memory, Intel recommends using memory that adheres to the Jedec memory specification which is 1.2 volts, plus or minus 5%. Anything over this voltage can either damage the processor or significantly reduce the processor life span.
There are no new chassis requirements for the Intel® Core™ i7 Desktop Processor Extreme Edition platforms utilizing the LGA1366 / LGA2011 / LGA2011-v3 sockets. Currently available chassis tested to support 130W / 140W processors should meet the requirement. The use of a Thermally Advantaged Chassis (TAC) is still highly recommended.
The Intel® Core™ i7 Desktop Processors Extreme Edition and the desktop boards that support these processors typically do not support ECC memory. ECC memory is usually used on servers and workstations, rather than on desktop platforms. This is mainly due to the price premium of ECC memory. Check with your desktop board manufacturer to see if ECC memory is enabled on your board.