Great to have you here! (sudden influx of new people much?) I was in the same shoes that you were a few years ago so I daresay that I could help you out. If you have any questions that you’d like to talk one on one about with someone then feel free to shoot me a PM 
James did a great job, so I’ll just throw in my two cents in case of tl;dr and reaffirmation. Also I might add that your post is quite well worded.
“if all the people who received government benefits were suddenly forced to get a job in order to survive, how would the economy benefit when these former beneficiaries are looking for jobs in this economy where finding employment is so difficult?”
To the supply and demand graph!!! (economy bat signal)
The laws of supply and demand work in practically all cases, this is no exception. The upwards sloping line is supply, the downards one demand. In our example more people would need jobs, this would mean that the supply of labor would shift to the right, or become more plentiful at any price. This unfortunately requires wages to fall, however because of this quantity and price both increase, this means that the quantity of goods produced by the economy rises and their price falls. So as for your first question: The economy benefits because more goods are produced which in turn means that real wages rise because for the same amount of money you can by more goods (supply and demand again)
As for how they would find jobs in the first place, we would have to pray that minimum wages would be repealed, see the milton friedman video on the subject. Let’s just say that minimum wages are generally the stupidest economic ideas that exist because they increase the cost of poor people’s labor without increasing their productivity. Fail. At any rate there are then two things that could happen, the first being voluntary charity by other people, which I think would be a lot more prevalent if we stopped relying on government, and secondly a fall in wages. The people who were formerly on welfare would have to accept fairly low wages, below what the market rate was pre-cutoff. With this being said costs in general would fall as a result of their addition to the workforce, somewhat cushioning their impact. So many would benefit, but those on welfare may well lose.
“Couldn’t a certain x amount of jobs be created without destroying any as long as the tax per citizen is low enough, which depends on the number of citizens in the area and the number of jobs created?”’
To put it simply, no. In this instance (because we are talking about overall employment levels) the economy actually does work like a pool. This is usually a gross error, but it’s as though you’re scooping out water and then pouring it back in, you can only put as much money back into the economy as you take out.
“why wouldn’t this work with a progressive income tax (not that I am assuming that this plan would work in the previous situation)? At least that way, smaller business owners would not get hurt as much.”
Now that depends upon how ‘progressive’ ‘progressive’ is, now doesn’t it. In our current situation this might not be the case because one could argue that the highest income brackets which save more have stockpiles of money which specifically are not being spent because no one wants to start a business in this atmosphere, but under general equilibrium conditions you take away from the rich, the rich have their money invested or saved, if it’s invested then you’re just taken money that would have been invested (a form of spending) and spending it somewhere else. 0 sum once again. If you inflate the money then you’re only confiscating it from one area of the economy because prices rise, the same effect occurs when you work with savings.
“http://www.youtube.com/watch?v=7gHpYUO4u5g”
She never actually answered the question of how it is that an increase in the minimum wage wouldn’t increase unemployment. She sort of shuffles around this by saying that there will be modest increase in prices but this is assumin a number of things, the first is that the new price structure won’t encourage skilled workers to be hired instead of unskilled, that the modest price increases necessary won’t result in a decrease in net yield (why is it that these places don’t just up their prices anyway if they will get this extra money?) and that the price increase will be uniform throughout these various industries. For instance higher class resraunts will begin to look more appealing because their above minimum wage employees won’t need an increase in pay and their prices need not be raised. Finally it will be the smallest start up businesses that are hurt the most by these sorts of increases. You can’t change economic laws like this. Sorry.