Class H1B valid from xx/xx/2008 to xx/xx/2011 by USCIS, why I cannot work to 2001?
-Because you went out of U.S. and got a new I-94 (it will expire on July 2009), your H1 status will expire on that day (July 2009), not 2011. You need to renew your H1 status before July 2009 (extending your H1 again to 2011, the date of your 6-year H1 ending).
2) Can I tour to Canada or Mexico to get an H1B visa?
-Yes, you can either file H1 entention before July 2009 or go out of U.S. (Canada, mexico, or China) to get an new h1 visa and come back with a new I-94 before july 2009. But you need to get a new passport first so that your new I-94 duration will be 2011.
Does it have time limit for stay in Canada or Mexico?
-No.