You are correct in that you can only be outside Canada for up to 3 years in a 5 year period, 1095 days to be exact.
a) You would be able to apply again but be aware that the rules may have changed and you may have a harder time qualifying now (or easier).
b) A day spent in the US does not come off your residency as long as you stay in Canada overnight. To facilitate easy border crossings, you should get a Nexus card, see
http://www.cbsa-asfc.gc.ca/prog/nexus/menu-eng.htmlYou would file taxes in both countries but because US and Canada have a tax treaty, you will not be double taxed.