ILR Help! unpaid leave and unemployment gap

Hi everyone I have a question and hoping someone in a similar situation can help-
My five years for ILR completes in Aug 2022 and I have a valid BRP until beyond that. However I have resigned my current position and am serving my notice period until October end. My next employment starts in January 2022- question is-
i) do I need to be employed for the 2 months gap period between both jobs? Will my visa expire and can this cause an issue for ILR?
ii) Can I travel outside the UK and return during this gap period? My BRP is valid until beyond 2022.
iii) I took 3 weeks unpaid leave this year. Can the 60 day unemployment gap add to the 4 week unpaid leave cap and impact ILR?

I am aware that the 60 day employment gap rule was scrapped but am having difficulty finding more information online concerning my queries above.

Has anyone gone through this experience and can share if they had any issues with ILR?

i) No. Your visa expires when it expires or it may be curtailed by UVKI. You must secure a new skilled worker visa before starting your new job
ii) Yes you can
iii) There is no impact

Tier 2 rules were changed in 2018 and now the Tier 2 route does not even exist. Here is the guide you need now: https://assets.publishing.service.gov.u ... 2.0ext.pdf

Zimba- thank you so much.

For #1- I am a doctor in a training program with Health education england (HEE), who are my sponsor. I am only changing my training program so my sponsor remains the same and no new COS would need to be issued. With regards to finding another skilled worker visa given that I am still under sponsorship with HEE, do you happen to have any idea in this situation? as in do I need to secure another visa for the 8 month period before being eligible for ILR?

Also- is there any helpdesk contact number of the home office where one can call for advice? If yes, can you please share. Many thanks

Then there is nothing to be concerned about. NO need for a new visa if your sponsor does not change. There is no immigration helpline