1.
refer to this document, especially page 32 about what you need to do:
http://www.ukba.homeoffice.gov.uk/sitec ... iew=Binary
the 60 day period will start from the date UKBA make the decision to curtail. It is not possible to predict when that will be but it is reasonable to assume that it will be at least 28 days from the time your previous sponsor reports your termination.
2
Provided the new sponsor has a) a sponsor licence and b) an allocation of unrestricted CoSs for the current year the assigning of a CoS is only a matter of minutes.
3
depends on how you submit your application, e.g. premium service, priority postal or ordinary postal.