No. After you have installed EQStitch one time, you only need to install EQStitch (not EQ7 first) for all subsequent installations. So just use the EQStitch DVD to install instead of the EQ7 CD. EQStitch will install EQ7 for you, as part of EQStitch.
You will need:
No, you only need to install EQStitch.
Yes, you can install EQStitch if EQ7 is already installed. EQStitch will convert your EQ7 into EQStitch. You will not be able to use each program separately since EQStitch is a plug-in, not a separate software.