Changing job

I am working permit holder Malaysian who working in singapore. If my last day in current company is on 24 Dec 2018, the working permit will be cancelled by MOM after current HR issue to MOM.
I change job to a new job. I have signed the appointment letter last week. They offer EP pass.
I wanna ask that:
(a)is that possible the application of EP affected when WP cancel within same periof?
(b)After cancel WP, i just can stay a week in singapore. Once i leave from singapore, can i enter back Singapore with use of the offer letter from company ?
(c) How long EP application process?

You should have read the many applicable posts on this forum first, then you would easily have found the answers:
(a) An EP (or any other work pass), once issued, automatically cancels your previous WP. If, however, the WP expires before the EP is issued, there is no influence (and you have to bridge the time inbetween with another pass).
(b) The offer letter is not an entry visa, thus does not help at all when entering the country.
(c) An EP application usually takes 1 - 2 months, but it can be more or less in certain cases.