I think your lawyer has point.
1). I quit my job so will I be able to apply for work permit extention?
You should apply as bridge work permit not extension. Extension would be the one to continue working with same employer...extend the contract or so.
2). Can I work after work permit application?
Yes, bridge work workpermit allows that.
3). Will I be allowed to enter in Canada if I come before 2 days of expiry?
As your lawyer said, you must come as early as possible. I would suggest to apply bridge work permit or extnesion right now. NOW and have all that proof with you when entering. I think you will be allowed, if you do all that properly and complete asap.
4). If I applied through a lawyer for express entry can I apply by my self for an extension?
You can but you are running out of time. Since, you need all the information of your PR application and need to apply online (everything and asap), probably, it will be best if you apply from your same lawyer.
5). What is the processing time of application?
You can check processing times here:
https://www.canada.ca/en/immigratio...vices/application/check-processing-times.html
It is fair bit of long time. Apply online - not paper.
6). What are the documents will I be needed?
If you go online application, you have to answer a number of questions and it will give a tailored list of documents. Basically, it is work permit and you will have to submit the PR application documents for bridge work permit.
Please provide me a expert advise.
I am not expert. For the expert advice, you would need to talk sam lawyer I think.