Hi George,
I've been through this just a year ago, here's my insight.
The sec. deposit is factored into the HUD statement at closing. So if you're buying a duplex that is rented out, the amount you bring to closing will be reduced by the amount of the security deposits.
No problem asking questions - I also use the inspection time to ask questions if the tenants are there...I usually ask about outstanding maintenance requests and/or problems they've had and the tenants are almost always more than willing to spill everything they know.
Not sure about finding out about moving in/out during the spring...if they move out you could be more selective about who you let in there next spring though (family vs. students).
Yes, although I don't personally see a problem with this, I think it's more of a etiquette thing.
25% down is what I do...based on this i'm assuming you're doing conventional financing. It takes me a year to build this back up for the next one, but for a long term strategy I feel really good about having 25% equity minimum starting out...the odds of my little empire falling apart feel lower than if I had 0, or 3, or 5% equity in a home. If something happens and I need to sell one or more off, it's not likely that i'll be under water..you just never know. Each one you buy helps buy the next one, it snowballs fast. As far as getting a home equity loan, it wouldn't be easy on an investment property using a normal bank, they just typically won't go to 90% LTV like you could with a primary residence.
These are my experiences and thoughts as a fellow Wisconsinite, I hope this helps.
Lucas