What, this part?
“4) some tell me there was no cause, because there was no “before” for the cause to exist in
5) But if that is true, “why” did the big bang happen at all?”
I repeat that I think it’s misleading to say that the Big Bang happened, since linguistically this attempts to put the Big Bang in our everyday life of each time having a before and after. Better, I suggest, to say that the Big Bang exists as a place in the universe. It is difficult, but possible, to divest oneself of temporality and consider time spatially, though it requires much patience.
No, I’m not. We happen to live on the Earth having this shape out of various shapes. I suggest that this region of the universe is similar. We live in the region of the universe having three dimensions of space and one of time (which can be treated as being a fourth spatial dimension), ie. having “this shape”. This shape is such that T<0 is like “north of the north pole”. There is no mysterious “land of nothingness” there - when cosmologists say there was nothing before T=0 they mean that there is no such thing as before T=0, not that there was a nothing-to-something transition.
If this is merely the shape of the universe, then asking what caused the universe to expand is directly equivalent to asking what causes the Earth to expand out to the equator from the north pole. I suggest “cause” is the wrong word to use, understandable though it is to use it since every configuration in our everyday lives does have other configurations either side of it.
You presented what I consider a false dichotomy: either the universe has always been in motion, or it was caused. I suggest a third option: that the universe has always existed, but the last 14 billion years is the only place where change occurs (and therefore, where time exists). This requires neither a first cause nor perpetual motion.
(Indeed, there are many instances of “timelessness” in the universe now, such as the reference frame of a photon or the event horizon of a black hole.)
If something has always existed, ie. never not existed, it requires no cause, agreed? Thomas Aquinas even suggested this 1000 years ago. We might seek to explain the nature or history of the thing that has always existed, but an explanation of its creation is unnecessary, yes?
Hence the title “A brief history … of time”.