Republic = Res Publica = Public Thing, Public Affair. It means the state belongs to the people
Democratic = Demos Kratia= Rule by the people (literally: the power belonging to the people of the community)
Both are correct to describe the USA. Technically speaking, the USA is a Representative Democratic Republic (you can also add "Constitutional" in there, if you like).
You know that piece of paper that starts with "We the people"? That pretty much defined it as a democracy. Maybe you are confusing it with Direct Democracy (as opposed to Representative Democracy), where everything is decided by direct vote by the whole population.
Now, about your arguments. Comparing "Google Glasses" with "slavery or death" is kinda funny, really. But I understand the point you are making. The point, however, is quite different. Requiring 4/5 Majority (or 100% majority) is not feasible, and it is actually not required for most decisions, not should it be. It would ultimately lead to anarchy, following the total collapse of a frozen system.
Your last argument of not being able to vote with your wallet to trump someone else's rights is valid, but based on a faulty assumption. You are working under the assumption that it was already decided it violates other people's rights, and the jury (and the people) is still out on that one. And one of the ways people express their decision regarding that is with their wallets. So what they are ultimately voting is on the question of it violating their rights or not.
Stay in school
Thank you. That is good advice for everyone. They even have some very good books on State Theory that cover all these subjects quite well. You should try one, if you haven't already.