Some users have recently had their accounts hijacked. It seems that the now defunct EVGA forums might have compromised your password there and seems many are using the same PW here. We would suggest you UPDATE YOUR PASSWORD and TURN ON 2FA for your account here to further secure it. None of the compromised accounts had 2FA turned on.
Once you have enabled 2FA, your account will be updated soon to show a badge, letting other members know that you use 2FA to protect your account. This should be beneficial for everyone that uses FSFT.
No, you may cause damage to either PC, the USB/Firewire hard drive controller(s) or the drive.
Then again it might not cause any damage but it sure wont work how you want.
If you want simultaneous(ish) access, get a NAS enclosure for the drive.
Or mount the external drive as a network share on one PC and allow the other access.
Assuming Windows, right-click the drive and pick Share from the menu. The rest should be obvious if you have basic reading comprehension. Then the drive will show in Network on any other Windows machine on your network.