I have a couple of questions:
1) My Vita downloaded the 3.61 firmware (still not installed). Is there any way for me to delete this firmware?
2) I have two memory cards, each one assigned to a different account. Do I need to update my system to switch the memory cards and accounts?
1. Yes.
2. I don't think so. Though I'm a single account user. You can connect to PSN if need be on 3.60 currently thanks to a patch.
Nobody has been banned but I'd personally avoid connecting to PSN more often than absolutely necessary.
I've dabbled in homebrew any time I could in the past, but it's weird how paranoid I am when it's a "connected" console.
If you want you can block PSN on your router or turn off wifi and use the offline installer. That way there is literally no way for Sony to "see" you.