I'm forming a software/web development company where we develop products and also help other business develop theirs. Microsoft offered us BizSpark membership. Is Microsoft now a partner to us or just BizSpark or we are not partners at all? What do we list them under our site as?
Yes you can list BIZSPARK in your partner list.
They even offer a set of logo here : http://www.microsoft.com/bizspark/Startup/DownloadLogos.aspx (you will have to log in)
However is is explicitly prohibited to list microsoft as a partner if you are only part of Bizspark (in the agreement you signed when you enrolled).
I would leave it out. Most savvy people looking at your website know that Microsoft has millions of meaningless partnerships and will not be that impressed by your listing of Microsoft as a "partner."
Professional Memberships?
It's not a partnership - they've just offered you a service and set of tools. It's more like a doctor belonging to a particular medical association.
You can, but dont.
It makes you look very very small.
Just like Microsoft as a partner, and if they ever complain say you meant the bizspark part...