So what if I just said "hey you are a N*****" to every black person I saw. Is there nothing in your legal system to stop me from doing this?
That is correct.
What if you are not inciting to violence but inciting to rejection of a group of people (ie no blacks allowed to use our shops or no Mexicans allowed to eat in our restaurants)?
This is treated as a very different issue from "speech". If you have a business which is open to the public, you are restricted in your right to pick and choose which members of the public you can let in: flat-out racial or ethnic exclusions, such as you cite, are always against the law. Discrimination in housing depends, again, on whether you are renting to the public at large, or renting part of your own dwelling-space: you can accept or reject anyone you want or don't want, for any reason or none, if you are taking in a roommate or a boarder into an extra room in your house; but cannot discriminate on basis of race, ethnicity, or religion in rental properties where you don't live.
I am trying to understand where government steps in to protect people, is it just when violence comes into it?
Speech can be restricted if it involves libel (false statement of fact, not just negative opinion), fraud (in a commercial setting, this is much broader than the libel exception in a private setting: statements which are technically true but misleading are considered fraudulent), or solicitation of crime ("I'll pay you $10,000 to kill my wife" is of course an illegal thing to say anywhere; it gets trickier if the crime is not one of violence, or if there is no individual targeted); and "time, place, and manner" restrictions can be applied, if they are uniformly applied without regard to content (repeatedly shouting the N-word on a public street is "disturbing the peace", but equally so would shouting anything else).
How much influence does your government have over state law? This of course isn't an issue over here, we just have one legal system but it appears in the US states can have different laws?
Very different, and the federal government has absolutely nothing to say about it.
Wow. So people are left to police themselves, even though someone died.
No, of course the person who actually stomped the kid to death was arrested by the police and put in jail for life. Going after the organization, however, is not appropriate for the government. Are you comfortable with letting the government, rather than the people, decide which kinds of political parties should be allowed to exist?
So if I was American I could stand on the steps of the Whitehouse, burn the American flag and say I hate all N****** and the government could not jail me?
As a security matter, you can't demonstrate "on the steps" of the White House no matter what point you are trying to make ("time, place and manner" restrictions have to be content-neutral). You can stand in Lafayette Park across the street from the White House and make any kind of point that you wish to make: it would be a rare day indeed when there was not someone there who appears completely lunatic. Most decidedly the government may not jail such demonstrators: that is the founding principle of our country.
So how have the government been able to keep that lunatic Christian family away from the funerals of American soldiers (I believe they have to keep a certain distance away, yet they have not called for anyone to kill American soldiers have they)?
As a "time, place, and manner" restriction requiring anyone uninvited (regardless of who) to keep a certain distance from a funeral.
The Bushies tried to justify keeping demonstrators a certain distance from the President on the same type of grounds, but lost since people with pro-Bush messages displayed were allowed where anti-Bush messages were not, violating the principle of "content neutrality".
I was just trying to understand why a black person can get on stage and say the N word every 5 seconds, without any media or public reaction, but a white person can't.
The media and the public actually argue about that precise point quite frequently and repeatedly.