T2 to T5

I hold a Chinese passport. I currently have a T2 work visaa which will expire in 2021.
I want to change my job and recently got an internship offer from another company. I need to resign my current job and apply for a T5 visa for the internship which will start in March.

1. Is it possible that I apply for a T5 visa and finish my internship successfully in March?
2. I know there is a cooling off period which means that I cannot enter the UK for 12 months. Does this period starts from my resignation? If I have a T5 visa, will my stay in the UK for the internship be counted into this 12-month period?
3. Can I apply T5 in the UK? and how long should I wait before getting it?

I am very worried about this problem. Hope someone could help me!!!

Many thanks

I'm not sure an internship is approvable in tier 5.