Yes, you can be a member of multiple ISD Teams. However you might want to think about it, this would get you extra responsibility and require more of your time to keep up with the requirements.
Yes it is. However when creating the ISD account, all you have to do is choose the Name, create you character like you normally would, and CCP will set everything up for you, like adding the “ISD” to the character and grant access to all relevant tools that you need to do you “job”.
Not sure what you mean by this? If you mean be ISD and have you player account(s), the answer is yes, but as stated, you may not be on your player accounts while doing ISD work.
To be perfectly clear, under NO circumstances can anyone find out the affiliation between ISD account and Player Account(s).