Line drive hits runner
 

Last night, 6th inning (final inning due to a time limit). Men's SP.

R1 on first base. B2 hits a line drive which hits R1, who left and just got back onto first base when he was hit (this is disputed by the defensive team). F3 was behind the bag and might have had a chance to make the catch had the ball not hit the runner.

What is the correct ruling?

We ruled the ball dead, runner is awarded 2nd base, batter is awarded first base. This ruling was based on my partner going to the state UIC for clarification earlier this team when the same thing happened to the defensive team.

What would have happened had the F3 been playing in and the ball was already by him, or he was nowhere close to being able to make a play?

The previous time it happened, it was a tie game, bottom of 7 and the bases were loaded. Ruling was ball dead, runners advance one base and the winning run was forced home.

Not out unless intentional. Correct for fielder being behind base, live ball if fielder in front of base. Only forced runners advance/

Outs, inning, score, disputes don't matter.

Why would the ball be dead? The ball is killed by hitting a runner when
a) the runner isn't in contact with a base
and
b) it hasn't passed a fielder OR it has passed a fielder but another fielder has a play on it

(this also answers your other question.)

Since you killed it that's an inadvertent call of time, sort it out accordingly.

For USA, RS 44.A 4th sentence.

I actually found the answer to this after I found an online copy of the rulebook.

The answer is in rule 8-1-E Effect 3.

Since the ball had not yet past the fielder, the ball is DEAD.

This rule is referenced by rule 8-8-M

Just a clarification, in the case of a runner being in contact with a base when hit with a fair batted ball, the status of the ball and the effect depend on whether the closest defender is in front of or behind the runner.

Though not likely, a defensive shift of some sort could place a fielder closer to the base than the defender assigned that area.

Agreed. I think in fast pitch you are much more likely to see a situation where the fielders are in front of the base. In men's fast pitch they generally are well back, as they were in this case.