Can you extinguish a fire on Shabbat to prevent property damage?
The Rambam is clear: financial loss doesn't justify extinguishing. You may build barriers to contain the fire, but not put it out directly.
Question 2
A non-Jew comes to extinguish a fire in your home on Shabbat. What should you do?
The Rambam rules: don't instruct them either way. If they come on their own initiative, you don't need to prevent them — but you may not request it.
Question 3
What three conditions must be met for carrying (hotza'ah) to create Torah liability?
All three must be met: (1) pick up in one domain, (2) place down in another, (3) minimum shiur carried in a normal fashion. Missing any one = no Torah liability.
Question 4
In a public domain, how far can you carry an object?
Each person has a 4-cubit by 4-cubit personal zone in the public domain. You may carry freely within it. Beyond 4 cubits = Torah liability.
Question 5
Does throwing an object from one domain to another count as "carrying"?
Throwing, handing off, rolling — any transfer from one domain to another creates the same liability as physically carrying.