Switch from Tier 4 to Tier 2 - Question about dates

Hello Everyone,

I came to UK in Sept 2016, and was granted Tier 4 visa for the period (Sept 2016 - Jan 2018).
According to my CAS, the program End Date is 30/Sept/2017, which leaves 4 months on my valid tier 4 visa.

On November 2016, I was hired by company x given that I can work full-time if my program has ended and I received my first payslip on the end of November 2016.

After one month, I was issued CoS by the same company x, CoS work start date was 11th of Dec 2017, however, my application approval was sent to me with BRP dated on 19th of Dec 2017.

1. How should I explain working on November (on tier 4) while Dec-present (on tier 2) when applying for ILR after couple of years? cover letter should be enough?

2. Is it ok that I started working on 11th while waiting for visa ? given that my "one day" appointment was scheduled on 6th of Dec ? Or should I have waited until I received the BRP?