“Bugger” is common in both Aussie and British slang, and vaguely refers to someone or something that is annoying. Calling someone a bugger can be used affectionately or derogatorily. The general expletive can be used in any situation, and roughly means,“F*** off/me” or “Well, I’ll be damned!”
F*** me dead
Basically, this means, “Didn’t see that one coming!” or “Oh my!” As you may have realized, profanity is pretty universal in Oz, which is why this phrase is a common way of conveying surprise.
An Australian version of "Go f*** yourself", in acronym form. A universal phrase, indeed.
Fair suck of the sav
The word "sav" is short for saveloy, or a red, seasoned sausage -- this is what's called a metaphor in literary circles. Aussies typically use this phrase when they think someone is being unfair, roughly meaning "Give me a fair shot”. Former Prime Minister Kevin Rudd famously gained attention for muddling the phrase as “fair shake of the sauce bottle, mate.” We understand what you were getting at, Kev. Idioms are hard.