Tier 4 PhD student visa curtailment

[mathew88]

I am 1st year PhD student in UK. My visa will expire in 2020.
However, due to my failure in defending my proposal in the exam, the University excluded me from the study with a letter dated 25 September 2017. The letter said that within 10 working days the university will inform the Home Office about my status. My understanding is that my visa will be curtailed and I must leave UK within 60 days when the Home Office issues a letter of curtailment.

My questions are that
1. I am appealing the university decision. Can I stay over 60 days to have the result of my appeal?
2. I am also applying for a new PhD at another university. Do I need to have the letter of curtailment for the new university to issue new CAS in case my application is successful? If I get a new admission by the new university, can I stay in the UK and apply and wait for a new student visa?
3. During the 60 days period, do I have still the right to work part-time in the UK?

Thank you very much.