1) I got my PR card in May 2010. Does this mean my PR expires in May 2015? How is this duration calculated?
In order to keep your PR in Canada, there is a residency requirement. The requirement is that you live in Canada for at least 730 days in any rolling 5 year period. The first test is if you pass the requirement in your first 5 years as a PR. This would be Nov. 2009 til Nov. 2014. From what you say, you are unable to meet this requirement. You say that you have not spent any time in Canada yet and you only have 1 year and 5 months left to your 5 year PR anniversary in order to meet a 2 year requirement to stay.
2) Am I allowed to enter Canada with my current PR card? (even though I still have time before it expires)
Yes, you are, however, see my reply to 3)
3) I am unclear about the statement "If they let you enter without reporting you" - Does this mean once I arrive in Canada the border officials will notify immigration department that I have a certain duration of stay left and deny my entrance to Canada?
The immigration officers must let you in because you are a PR with a valid PR card. However, if they suspect or you admit that you are unable to meet the residency requirements, they could report you for it. If they do, they will still let you in but you would have to appeal for your PR. Getting reported is however not that common and the more time you have left until your PR card expiry, the less likely it is to get reported.
4) If I can enter and stay in Canada. What happens after the current PR card expires? Currently I have about 22 months (July 2013-May2015) time left on PR card.
Nothing happens when your PR card expires. There is no law that says you must have a valid PR card to live in Canada.
5) What should I do after the current PR card expires when I am in Canada? Can I reapply for a new PR card or request an extension or some other process?
If you get into Canada without getting reported, you should stay for 2 years straight like I said in my first reply to you before you attempt to renew your PR card. If you try to renew your PR card without having 730 days in Canada in the past 5 years, you would bring it to immigrations attention that you do not meet the residency requirements. You absolutely do not want to do that. You want to wait until you have 2 years at which point you will meet the requirements. Then you can apply to renew your PR card.
6) If I am not allowed to enter Canada, is it better to seek a TRV beforehand to enter Canada? Can I ask for a 2 year TRV? Will this affect my current PR card? Can the 2 year TRV be counted towards my current PR card?
You can not get a TRV if you are a PR. If you want to renounce your PR in order to get a TRV, you can but there is no reason to do that at this point. If you want to keep your PR, you should move to Canada now and stay for 2 years. This will bring your PR in good standing again.
7) If I am allowed to enter Canada on current PR card and I find employment, what happens past the PR expiration date? What can I do to maintain legal status? Can I reapply for new PR card during the last year that is left on my current PR card? Will this affect employment status or legal status? What should my employer do?
See reply to 5). Your PR card expiring does not mean that your PR status has expired. Your PR status is valid until you renounce it or immigration revokes it. If you get into Canada without being reported and stay in Canada, stay within the law and don't apply for anything from immigration, the odds of your PR status being revoked are almost zero. As long as your PR has not been revoked and you have not renounced it, you are perfectly legal to live and work in Canada.
If you do not yet have a social insurance number (SIN) you can apply for one after your move. The SIN is all you need to work in Canada. Your employer does not need to ask you about your PR card and it is not their business when it expires. You should definitely NOT try to renew your PR card when you do not meet the residency requirements. Your employer can not ask you to renew your PR card. All they should care about is that you have a valid SIN.
If you are not sure where to move to, I suggest Alberta. First day health care, low unemployment.
