In America we usually take an eisegetical approach to the Constitution. But how would a strict constitutionalist view taxes? I have my own (probably unoriginal) theory using some context of the time but I'll wait until this gets a few replies.
If a guy broke into your house, and you caught him, what would you do? Would anything change if he told you he gave himself permission to steal your TV?
False analogy. A representative democracy is a very different thing.
Yours is a libertarian bromide. At best, you could make a case that it's extortion. But it is not theft.
You should be arguing how to make the necessary functions of government fair, efficient and constitutional. Focusing on the "Taxes are Theft" angle is to invite logical inconsistency, and puts you not with Libertarians, but with anarchists.
Most western countries, including the US are representative democracies. Within that, we are a federal republic.
You are picking at the wrong nits. Representative democracy is the broad category, into which different flavors (eg. representative republic - additionally a federal republic) set.
Not changing the term. It's a subset. E.g. humans are mammals, not all mammals are humans. Not all democracies are representative republics. All representative republics are also democracies.
No - but they are both "motorized vehicles"