No, let's return to the 2 definitions I noticed you edited to fit your argument.
Yes, let's do that and see what we find.
Notice that our governing body is split unlike a parliament.
Parliaments can be unicameral, bicameral (the British parliament is bicameral, just like the US congress) or have other structures, more or less complex. The congress is a form of parliament, and more importantly it is precisely the kind of governing body that the definition of democracy refers to.
And absolutely nothing in that definition excludes a republic from being democratic. Or should I interpret your use of boldface as you considering a democracy to be a government exercising power in absence or violation of law? And if that's the case, where do you find support for such a definition of democracy?
Again, as it seems like the bus analogy wasn't simple enough: republic and democracy are not mutually exclusive. Just like a bus can also be a vehicle, a republic can also be democratic.
You attempted to conjure them as the same thing, and yet, if they were, they would fall under the same page. You've also altered your argument from "we're a democracy" to now, "we're a liberal democracy" because it fits your argument better.
Liberal democracy is a form of democracy, just like a sports car is a form of car. The US is a democracy, and it's a liberal democracy, and it's a presidential democracy, and it's a federation, and it's a republic, and it's a federal republic. Just like you are a human, and an American, and an organism, etc. Things are very rarely just one thing.
And continuously forget the basic difference between "democracy" and "republic" to begin with.
They are different terms, but again: not mutually exclusive.
A Democracy would have resulted in Hillary being elected because the citizens voted for her in the majority.
Not at all, it doesn't have to be a direct vote. Voting for someone to represent you fits the definition as well, just look at the use of parliaments.
As for the electoral college, some may claim that it would be more democratic to have a direct vote, while others may claim that such a system would favour the big cities on the expense of rural areas and smaller towns. There is nothing that suggests that one of these systems would be more democratic than the other.
The key component here is that there is a free, fair and public election.