I think Harry Frankfurt’s distinction between lying and bullshitting is quite useful; the German words I mentioned, especially Mumpitz, Firlefanz and Kladderadatsch, follow a similar thought, though they differ in meaning and usage.
Yeah. A better explanation than my own.
Old Navy joke:
Do you know the difference between a Fairy Tale and a Sea Story?
A Fairy Tale starts out: “Once Upon A Time”
and a Sea Story starts out: “Now This Is No Bullshit”.
Bu shi is far, far, far too polite. 
Bu shi sounds about as hoity as “No it is not”. BU! Would be more forceful.
Approximately correct. Although, the typical phrase would be more like “what dog farts you’re letting off!”
Wikipedia tells me that “fang pi”, or fart (farting), is also used - I’d almost forgotten!
In Finnish we say “puhua paskaa”, to talk shit, said words being “paskapuhetta”, shit speak. Something can also be “hevonpaskaa”, horse shit, but it’s a bit less common. If someone is trying to tell you something that is not true, you can also say they are trying to “kusettaa”, or piss you. Also “kusta silmään”, to piss in someone’s eye, is to deceive someone.
Of course, we have also appropriated the English expression into a handy verb “bullshitata”, which is used quite commonly to refer to, for example, what we Marketing students do in our exam answers. 
Do people in America say “That’s (utter) crap!” or “you’re talking crap!”? They’re pretty common in Britain.
While people in Scotland would know what you meant by “bullshit” I think they’d be more likely to say “that’s shite!”.
I know we use the phrase “talkin’ shit” in the South, at least. It could mean either bullshit or being provocative.
There’s also ‘hovno’, which is animal shit generally, but which is used as bull shit. There’s also ‘hnůj’, which also means animal shit, but which is used to refer to people.
Yes, occasionally, but that’s usually stronger than Bullshit! Bullshit! can be said with a grin, which softens it.
I would include a slight correction to this: you say “merde” to someone, indicating “good luck”, before they engage in the activity requiring luck, e.g. buying a lottery ticket, going on stage, etc. Kind of like how you tell an actor “Break a leg” in English-speaking countries. If they’ve already won the lottery, it wouldn’t occur to me to say “merde” to them - they’ve already had the good luck. It would be like telling an actor “Break a leg” after they come offstage and their performance is over.
The correct way of softening “bullshit” is by coughing whilst saying it, which makes it undetectable by people who might take offense and be in a position to censure you for your vulgar language. By coughing over it you can use it with impunity in any situation, e.g. in an argument with an angry wife.
As in Animal House?
What jovan probably meant is that in very informal Quebec French, if you call someone “merdeux” (usually pronounced “mardeux”), it means they’re lucky. Do not confuse it with “merdique”, which has a very different meaning indeed.
If someone says I’m “plein de merde”, though, I’ll assume they’re calling me a bullshitter.