Skilled Worker Visa + Change in Employer + Dependents Visa + Travel Outside UK

Apologies for the long post. I am confused and might be overthinking a lot. Please see my query below -

I was on Tier 2 General visa from Jan 2019 to Jan 2022 and extended my visa for further 3 years which is now Skilled worker visa until December 2024. This includes my spouse who is currently on dependent visa. (Current Eligibility for ILR is Dec 2023)

1. I have now submitted my resignation in Oct 2022 and the joining date with the new company is Jan 2023. I am planning to end my current employment in Nov 2022 and travel to India before i join in Jan 2023 and submit my new visa for new employment from India during this break. Can I apply the visa from India and does this break of non-employment from Nov/Jan impact my ILR? I am not planning to stay outside UK more than 60 days.

2. I have a new born in June in UK and we haven't filed his visa yet. I am thinking to apply my son's visa from India along with my visa. Will he be eligible for ILR in Dec 2023?

3. My spouse has a dependent visa (BRP) which is valid until Dec 2024, considering the change in my employment, does her visa also needs to be renewed or can she use her existing BRP to travel inside and outside the UK? Will that affect the ILR eligibility in anyway?

Thank you for your help.