First of all, you’re a citizen of the United States. You can be a /resident/ of a state, but citizenship is conferred by the federal government, not the states.
Second, you’re not paying the tax, the customer is.
Third, it is absolutely not taxation without representation, which was a charge the British colonists made against the government in England because they had no representation in parliament. You, however, have several representatives at various levels of government, as do your customers paying taxes. You might argue that your representation isn’t good, and depending on the state I’d argue that too, but you absolutely are not taxed without representation now in 2018.
Taxation does not entitle you to vote in elections. If I drive through Ohio and buy some gas, do I get to swing by again in November for the election? I don’t know the relevant legal philosophy, but states can absolutely levy taxes in other states and it’s ridiculous to suggest that paying them entitles you to voting rights.
Yes, because your intent is to circumvent the provided mechanisms of the Instagram API and you’re doing it with a program instead of just browsing around the site with the intent of using it like a normal user who isn’t scraping. “But the program did the exact same thing that a human could do!” is a really good, pedantic CS argument, but it’s a terrible legal argument.