From all those questions you seem to be struggling to understand how a society works. Don't worry, I'll help answer them.
But who formed the government?
If you meant the current government, then a group of people elected (directly or indirectly) by the adult populace of your country. If you mean the original government institution that's somewhat irrelevant since they're dead now - they aren't the ones making decisions today. The elected people are the ones making decisions today, and it should be possible to override any decisions made by the now dead people which aren't popular.
What happens if you don't pay your taxes, or declare yourself to be "independent" from your country?
For taxes: same thing as what happens if you break any other law deemed to be necessary by the democratically elected government. For declaring yourself independent: nothing at all, just like declaring yourself to be an 8th grade pianist or a wizard.
What, exactly, makes the government a "legitimate" institution?
Democratic elections among the people being governed. This isn't synonymous with morality though - for the conditions of it being a legitimate and moral government see below (generally the government should reflect the moral standards of the people electing it).
If everyone on my street has a vote to seize the property of a quarter of the people living here and we vote yes, are we justified in taking their things?
Assuming you mean morally justified then in this question the answer is probably no. However if a service is required to keep your entire street operational (let's say road repairs, firefighting) and some members of your street are gaining more money as a resident of this street (and thus as a result of this service) you are justified in taking a larger amount from them in order to continue providing this service. This doesn't stop applying if some of the services are only needed by some of the people, as long as everyone is relying on that same service to keep the whole street operational. If they do not feel they need these services they can move to another street. This is a more valid analogy to a government, and I can understand your confusion if you previously believed all the government did was randomly take 25% of the populations things.
In practice it's a lot easier to administrate over a much larger area than a street (otherwise each street would need its own accountancy and enforcement and fire brigade and so on - clearly wasteful when one fire engine can cover multiple streets, and one accountant can oversee the services for many streets) which is countries are generally larger than one street.
How about our town, our county, our province?
See above - a group of people could decide to form a societal unit of that size, but it would be wasteful. Generally you have some devolution to each of those levels to handle local issues, but having the whole thing overseen by a more centralized government is more efficient.
At what point do we cease to be criminal and become a government?
"Criminal" is a slippery term, tied directly to law. Assuming there was no state above you then you aren't actually a criminal at any of those levels since you had no laws to break. However I'll assume by "criminal" you mean "immoral/amoral".
If you follow the guidelines I said in the previous questions you aren't immoral/amoral at any of those levels. If you take your bad analogy at face value then you are amoral/ immoral at all of them.
What differentiates the government from, say, the mafia?
- Organized criminals are generally not democratically elected by the people in their areas
- Organized criminals do not care about the wellbeing of and generally do not even claim to represent the people living in their areas
- Organized criminals are unlikely to have mechanisms by which their constituents can petition them to change how they operate in an area
- Organized criminals do not provide services essential to a modern society
- Organized criminals do not operate according to a consistent set of laws set down by members of their society, and even if they did they probably would not have an accountable and democratic mechanism for changing those laws
- Organized criminals often do not let their victims stop paying if they leave their area (or they may prevent them from leaving)
Is the mafia legitimate if it provides services of some kind to those it extorts?
No - that is only one of the major differences between the government and your average group of organized criminals. If your question was amended to the following:
"Is the mafia legitimate if it provides essential services to those it extorts, has democratic elections to decide its members, care about the wellbeing of and represent the interests of those it extorts, have mechanisms whereby those it exorts can petition them to change their practices, operate according to a set of rules determined by their society with clear and democratic means of changing those rules and allows those it extorts to leave their area at any time?"
It might be answerable with "yes", although it may be something of a contradictory question as you've pretty much left the definition of "mafia" by that point.
The welfare state doesn't ultimately improve the lives of its people, it simply shuffles resources around and fools people into thinking their lives are improved. There comes a point where the welfare state is incapable of providing for its people enough to make the costs seem justified, and at this point people begin to resist. This point as already been reached in Greece and Italy, and it likely this point will be reached soon in the rest of the world, including both the USA and France.
This isn't a question but it is a hilariously unjustified assertion. I can now eat food and sleep under a roof but apparently the government is only tricking me, I was better off when I was sleeping rough and eating from garbage cans.