Verbal Obstruction?
 

R2.

F1 spins and fakes a throw to the covering F4. R2 dives back into the base thinking there is a throw.

F8 comes charging into "field" the ball that was never actually thrown. Defense starts yelling "third, third, third!"

R2 thinks the ball is rolling to F8. He gets up to run to third where he is tagged out.

Legal?

Yep.

Fake plays (aside from fake tags) are legal. Mimicking base coaches or talking directly to offensive personnel to fake them is not.

This is illegal in FED. Yes verbal obstruction.

I think the only examples in FED are where the defense says something that the offense would normally say.

It's unclear to me how far to extend that (if at all).

Case play?

This is a variation of the "Miami" play, and I got nothing to call in any rule set. I will need a case play or AR to consider this verbal obstruction in FED or any other rule set.

The one where the runner slides in and the defensive players start yelling "back back". Don't have books in front of me.

I think the catcher threw a pop-up with a runner stealing or something like that.

Yelling "back, back!" is something a coach would say. I agree that mimicking base coaches is verbal instruction, but I don't think this is that. Yelling "third, third!" is something the defense would legitimately say. I don't think I'd call the original situation verbal obstruction. If the runner and his base coach don't know where the ball is and they fall for the defense simply acting out what they legitimately would do in an overthrow situation, then shame on them.

Verbal obstruction
 

If a runner ran by a fielder camped under a fly ball and yelled "MINE" or something similar.
I have had a defensive coach yell "Walk" as the pitcher goes to his stretch.

2.22.1 SITUATION A: R1 attempts to steal second. F2, upon receiving the pitch, throws a pop-up to F6. F5 yells "get back, get back." R1 thinks B2 has hit a pop-up and starts back to first where he is tagged out.

RULING: This is verbal obstruction and R1 shall be awarded second base.

No it is not. Not sure why anyone would think it was.

yelling offensive commands to offensive players is one thing. The OP is not even close to this.

Interference and Obstruction are opposites.

Most of the time.
 

You are correct, however, there is catcher's interference.

Rule 2.00 (Interference (a)) Comment: In the event the batter-runner has not reached first
base, all runners shall return to the base last occupied at the time of the pitch.
(b) Defensive interference is an act by a fielder that hinders or prevents a batter from hitting a pitch.