Well that’s not true either.
Above a certain gain, you might just get more internal noise, but not more real signal.
No not really.
You don’t want the planes close by to overload your receiver.
Low and close flying planes are in the horizontal plane of the antenna (roughly).
Those can overload the receiver, you would see it on the local map as the track is interrupted.
And generally, with >5% of the red messages, often the message rate from close by planes goes down.