1) Yes, I think you are expected to pick up the disc if you signal a brick. The rule says the ‘intended thrower’ will signal, so by signalling you make yourself the intended thrower.
[From a purely logical point of view, you could argue that if you’re not the intended thrower, then your arm-raising was, by definition, not a ‘brick’ symbol, since only the intended thrower can signal – you were just stretching your arm! – so someone else could pick up. But this is very clearly not the intention of the rule.]
2) No, it’s not a violation. If one is fractionally ahead of the other, then they should become the thrower, but if they’re at exactly the same time then they should decide quickly amongst themselves who it will be. There is no advantage to a team in deliberately trying to both signal at the same time – both because there is ample time for the defence to react to any specific thrower in the time it takes to bring the disc to the brick, and because the same delayed decision could be achieved by neither player signalling until just before picking up – so there is no reason to write a rule to deal with this situation.
3) Yes, you should play from the brick if you have signalled to do so. It would not be permissible, for example, to signal a brick, and then play quickly from the sideline to surprise the defence. The exact wording of this could be tightened in the next iteration, perhaps, but clearly the rule is not intended to encourage deceit or surprise. The signal should be considered binding.