Switching employers while on skilled worker visa

I am on skilled worker visa with my current employer, but have an offer from another employer who have agreed to sponsor my visa. My notice period here is 2 months, and I am traveling outside UK on 18th of November to return on 23rd December, which will be during my notice period.

If I ask my future employer to apply via super priority route and get my new brp before November :

1. What should be the ideal start date on CoS assuming I want to start my new job in January? Will the new BRP be valid for travel and entry to UK starting from November?

2. Can I get a BRP now which states that the start date is in January (as per COS)? If so, will my existing BRP be valid for stay and travel till December as I will be serving my notice period anyway?

3. My spouse is currently on dependent visa, will she have to apply again as dependent with me if I switch employers? Or will her existing dependent visa be valid for stay and travel?

Any pointers appreciated. Thank you!