a) Does processing time of PR is different in different states of Canada.
Only if you apply through a provincial nominee program. Quebec is also an exception. They have their own immigration program but they don't call it a PNP.
b) I am a Mechanical Engineer and my wife did graduation in computer science so in which category of PR should we apply?
Any category you qualify under.
c) I am on H1-B status in USA. Once I leave USA I must get visa stamp on my passport to get back to US. If I do not get the visa stamped on my passport and had to stay in Canada, can I apply for PR in Canada. Will I have to go out of Canada to submit the application.
You can submit a PR application from within Canada but you will not have your PR by the time your visit status expires.
d) Can I apply for PR card while staying as a visitor in Canada. How much time will it take for my application to be accepted?(say 2 months ?) Can I and my wife do job in Canada and can my Kids go to school after the application is accepted?
Yes but you will be waiting for your PR much longer than 2 months. Try a year, maybe more. Once you and your family all get PR, your wife can work and your kids can go to school.
e) If I apply for a self employed business visa, what would be the procedure . As self employed I would be doing press printing (Business Cards, Advertisement cards, Brochures, Banners, Ads preparation, sign boards etc.), graphic design and web design.
I am not aware that there is such a visa available in Canada.
f) If I try to get Permanent Residence in CANADA on education basis and use employment category, how will it work in my case(mechanical Engineer) or my wife's case (IT engineer).
You would need a job offer to apply under the skilled worker program. If one of you gets a job offer and can qualify, that one could apply for PR for the whole family. Most immigration classes under PNP also require job offer. Quebec immigration does not require a job offer but in most cases, you would need to speak French to qualify.
g) What will be the expenses for PR.
Around $1000 per adult and $150 per child plus cost of medicals for you all, cost of photos, photocopies, translations etc.
h) How much time will it take for getting a PR. When will I be eligible to work in CANADA?
Depends on under which immigration class you apply under and from which country but generally not less than a year, probably more like 18 months+. Once you get your PR visa and "land" in Canada as a PR, you will be eligible to work. If you want to work sooner, you will need a job offer, labour market opinion and work permit.
i) If I am in CANADA for 6 month visit visa can I apply for a PR there. When will I be allowed to work.
You already asked that in d) and h)
j) Can I visit USA on the basis of PR only assuming that I have no other US visa (like H-1B etc)
No, a PR from Canada is not visa exempt to visit the US. You would still need a visit visa.
k) What should I do immediately to start the process.
Read the website somebody already linked to, find an immigration class you qualify under and apply.
l) If I am stuck in CANADA that is w/o any visa for back to USA, then what will be the course of action.
If they had let you in as a visitor, you can generally stay for 6 months unless they specified less time. You can use this time to look for a job, try to get a labour market opinion and a work permit. When your visit visa expires, you have 3 months to restore your status. You could also apply to extend your visitor status. If you don't succeed, you must leave.
m) What is the procedure of opening a branch office of a business already registered in USA?
That one I don't know.
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