SEGS helppppp

[Swan]

Hi All,
I have obtained my PhD from a UK university 3 months ago and my student visa is running out in 3 months. I want to apply for the Science and Engineering Graduate Scheme (SEGS), these are my concerns:
- What is the best time to apply in respect to the expiry of the visa.
- in case my application gets rejected, will I still be able to apply for another student visa providing the fact that I register for another course?
- The JACS code of the department I graduated from is not on the new HO approved list, however my course subject is on the list for approved courses. So I was provided with a letter from my university explaining this. Will I still be eligible to SEGS?
-if my application is succesful, and if i do not find a job within the 12 months of SEGS, will i be able to apply for a student visa after the 12 montsh run out?
Thank you so much