1. Does America's current two party system actually work for the American populace, or does it in fact work to the American populace's detriment due to necessarily forcing partisanship?
The two party system has been in place since little before the end of the Washington Administration. In short we've had this system longer then most nations governments can say to have existed. It pre-dates the governments of continental Europe, it pre-dates the governments of Latin America and Asia. If it doesn't work for the American people, I would have to ask why does it not work now when it has been working for generations. It is in the confines of the two party systems that radical and dramatic changes to American society have been affected. The victories of the civil rights movement and the women's liberation were not brought about by a 3rd party after all.
Frankly most of the people who claim this then proudly tell me that they don't vote and that they never had. Claiming they are shut out because there is no one representing their views. Honestly that is a fair gripe. The actual ideological representation in Congress is fairly narrow (Bluntly, the far right parties of continental Europe, Japan and India to name a few are to the right of the GOP, while there are acres and acres of space to the left regarding the democrats). That said, opting out ensures that no one will ever represent your views and why should they? You don't vote. No matter what the government does, you never take the most basic action in a democracy to correct. At best you will make some sound and fury that signifies nothing. For the average American, if you do not vote, your opinion does not matter to a politician. You are no threat to his job prospects. At best he will act to ensure you remain a non-voter through what will to him trivial action. Angry voters are a terror, the screams of nonvoters barely register.
Additionally if you can't be bothered? I'm pretty sure I don't want you voting anyways.
2. Is the influx of corporate cash in the form of non-profits and SuperPACs a necessary consequence of how the political system works here in the US, or is that a problem with another cause?
A consequence? Yes. A necessary consequence? Well now we're talking about something different.
The influences of corporations in American politics has waxed and waned over the decades. In the gilded age they were quiet open on their influence, the backlash of the Progressive era curtailed much of their domestic influence (Yes, I'm aware of the banana wars but frankly deploying armed forces to support economic interests is something just about every government that is strong enough to get away with it does. France certainly doesn't hesitate if it's corporations interests in Africa are threatened.). After World War their influence rose again only to fall under the heels of the FDR democrats and remain under those heels until the 70s/80s.
This is a simple problem brought about by the system of capitalism has practiced in the US (and China, and Japan, and elsewhere). Corporations exist to make money. If they can play with the laws, they make more of it. Governments make laws and tax Corporations. Corporations therefore attempt to ensure governments do what they want instead of the other way around. Nations have dealt with this problem in different ways, we tended to use rather soft handed regulations compared to others (I don't recall any nationalizations or executions for example).
The current situation is brought about because one group of elites has decided to represent the corporations desires in a large way and the other party hasn't decided to oppose it. This has happened because voters has a whole haven't demanded that anyone opposed them in a meaningful way.
What's that? Yes, they have? There was the whole occupy wallstreet and so on and so forth? Bullshit. The OWS movement refused to organize politically and wasted it's energy flailing about and being steered by jackasses with stars in their eyes. You'll notice that force was used on them... When it became clear that they were not going to become a political organization but rather a bunch of people griping in tents. They became no threat to the politicians job prospects and the police moved in and threw them out.
The tea party did organize as a political movement and they got treated with soft hands. You can scream billionaires all you want (what there are no leftist billionaires now? The Reverend King didn't happen to face an entrenched system of brutal elites who were determined to stop him? Cry some more! That'll Help!) but in the end, one side threatened to vote and got what it wanted and the other side threatened to stay in tents and got a billy club to the face. Figure it out.
To boil it down, it is a consequence of corporations wanting to influence the system for greater profit and no real determined political block opposing them. In our system if enough people with enough money or numbers or both get together and want something, they tend to get it unless another group is working really hard to stop them.
"it takes two sides to end a war but only one to start one. And those who do not have swords may still die upon them." Tolken