Skilled Worker Visa (Extension)

Hello Guys,
I applied for switching Skilled visa last year when the job offered by my employer (a university) was one year. However; the visa was granted was for 11 months. Now, I've still have around 2 months of my contract left and the university is willing to give me the letter for the extension. I've basically two questions
1. What's the maximum length of visa i can get when the contract is for 2 more months?
2. I've applied for a job vacancy (Which I would probably get in same university), however; the timeline doesn't match my visa. So my question is would i be able to apply for extension based on me searching for a job?
Please if someone could help!

1. Period of grant is subject to SW 18.1.

The applicant will be granted entry clearance or permission to stay until 14 days after the end date of their certificate of sponsorship (the end date of the certificate of sponsorship may be up to a maximum of 5 years after the start date of their certificate of sponsorship).

Did they make an error with the current period of grant?

2. If you make a valid application to extend or update (unsure what the difference is) before expiry of leave, then they will treat your current leave as continuing under Section 3C, until a decision.

Requires a new certificate of sponsorship, etc.

Yes they made an error of granting me 1 month less visa than what was on COS. Anyhow, my university (employer) is giving me a three months extension on the current job. Would it require a new COS for visa extension? Also, how long the new leave would be for? I mean would they only allow additional three months of a few months extra for a new job hunt? Please clarify

Thanks

You need a new CoS for an extension.

The visa will be valid for the same duration as the CoS.