Tenant Left Water Running & Overflow Caused Damage - Advice Plz

[Jeff Li]

First year landlord here.  I just found out that my tenant left the shower running all night while the bath was plugged.  Water overflowed to the floor, causing damage to my unit.  Not only that, this is a unit in a Condo building.  The water overflowed to the hallway, causing damage to the common area.  AND the water leaked all the way down, causing damage to multiple units in floors below.  At this point, Condo management is taking care of initial servicing and I'm going in Monday to assess the damage.  

Given my inexperience on a matter like this, I'm soliciting everyone's expertise here.  

1) How should I handle the liability with the building and other unit owners?  Through insurance company?  Through a lawyer?  Myself?

2) What kind of liability should I expect?  Is it enough to just repair the damage in the other units?  Or should I expect to be liable for more that that?  

3) Should I hire a lawyer to assess/protect my liability?  Tenant has admitted fault and building management will confirm that there is no piping issue that caused the overflow.  However, it's not in writing right now.  

4) How should I work with the tenant on this?  Even if he's at fault, I don't want to just leave him to deal with the other unit owners since I'm ultimately legally responsible for that unit; but should I make him financially responsible for everything, or can my Condo insurance be involved?  (He doesn't have renter's insurance)

5) One thing I'm concerned about is insurance.  I initially bought the unit for myself and had Condo insurance under my name.  After renting it out, I never converted it to a landlord policy.  Is that going to be an issue?

6) What kind of professionals should I be working with to help me assess and repair the water damage in my unit?

7) Any other suggestions on this matter would be much appreciated.

I have a feeling this is going to be a nightmare.  So thank you all in advance for your expertise!