I can't answer the first question.

I removed all of my money from my ING account a while ago, but kept the account open. There was no hassle involved except an additional interest payment I had to remove a little bit later (more money, darn? :P).

After doing so, I continued to receive emails from them about once every 3 to 4 months. They recently seemed to have changed that policy, though, and I was getting them once a week until I remembered my login info and changed email preferences. I haven't received anything since making that change in November.