Right month to join a new company

As soon as you get the offer

Ideally depends on when the appraisal cycle is in the next company. I think for most, if you join atleast 6 months prior to that you will be eligible for appraisal and not have to go to 1+ years without any significant jump

Depends on your next employer's performance cycle but how much control do we really have? We get offer, put paper, join as soon as the notice is over.