Changing Jobs and start date for new job to be eligible for ILR

Hi, I am waiting an offer from a new employer and would like to share the start date with them. My existing BRP is valid till Dec'23 and notice period in current firm is 2 months. I understand, we can not apply for visa more than 3 months before the start date of the job listed on the COS. I am planning to resign when i get the BRP for new firm as i will be applying for priority visa service. Could you please help to confirm below

1. What happens if my last working day is before the start date of new job? Will i be breaking any rule and will it impact my ILR?
2. What happens if my last working day is after the start date of new job? Will i be violating any rules which could impact ILR?
3. Is there a min timeframe before or after the start date during which I need to join the new company.
4. Any issue in serving the notice period of current employer once i have received the new BRP?
5. Does new BRP would have a start date same as Starting date with the firm?

Appreciate your help

1. No
2. No
3. You should start working no later than 28 days after the CoS start date or application decision date, whichever is latest, unless you are still within notice period.
4. No
5. It will be the decision date, i.e. the day you receive decision email.