Are these question from some mock tests or questions that you framed? Please post one question in new thread as it is easier to read and follow up on it. Anyways, Here are my responses:
1) The project is on tight schedule. Sponsors are in process of writing a charter. What should PM do?
a) Start working on Project scope etc or
b) ask team members to work on scope & schedule or
c)wait for charter approval?

Answer : option C wait for charter approval as without charter approval the project does not exist

2) Customer suggested change during execution which is out of scope. Customer insists of making this change without increasing schedule and budget. What is the next step or best possible answer in such case?
what are the options given ?
Answer : Possible option: As the question states, out of scope this implies that PM has already done his/her analysis. So ask the customer to start another project charter to work on additional scope.

4) A project (all the deliverables) has accepted by the customer. After that -
i) What if a Team member found a bug -: Quality assurance and quality control takes care of this
ii) What if deliverable product has a problem in production. - Not a part of the project
iii) What if Customer found something error/issue - This normally happens during scope validation
iV) If warranty is one of the choices in the question, then is it going to be handled by operations/warranty or say no to customer as it is already accepted or start a new project? - Not clear

5) The project is about to complete, before accepting the deliverable, customer asks for change in one of the deliverable. This requirement was not included in the scope.
i) What if Sponsor has denied this change before?
ii) What if customer is not ready to pay extra and insisting on using reserves?
iii) What if customer is not adding any time and money for this change? The time & money is available since project is ahead of schedule cost.
iv) What if customer is not adding any time and money for this change? The time & money is not available since project is on schedule and cost.
v) What if customer is not ready to provide final acceptance if the above change is not done
Answer: As requirement is not in the scope ask the customer to start a new project.