1. that's how the tax would be collected for most peope. ie. you'll pay $x/gal more at the gas pump, rather than declaring how much tons of carbon you emitted on your tax return.

2. whether they pay or not is irrelevant. what actually matters is whether they end up paying more or less in net. for a scheme that taxes people according to their consumption but gives everyone the same amount of tax credits in return, poor people would be expected to come out ahead because they consume less on average.