The Kalam Cosmological Argument

[Modern Atheism]

Quoting from Wikipedia: 'The most prominent form of the Kalam cosmological argument, as defended by William Lane Craig, is expressed as the following syllogism:

Everything that begins to exist has a cause.
The universe began to exist.
Therefore, the universe has a cause.'

I find this argument laughable because it's supposed to be an argument for God but the conclusion is just that the universe has a cause.

William Lane Craig usually does elaborate on why this cause is God. He says that: 

a. Being the cause of spacetime, this cause must trascend space and time itself
b. All mechanical things are bound my cause and effect. Only a mind making a decision out of free will can bypass this cause and effect rule, so such decision could be uncaused.

Regarding (b), I am not sure that a mind making a decision can be said to be uncaused. A mind making a decision is usually caused by a previous mental state, not uncaused.

Craig also talks about an infinite series of past causes being impossible, because an actual infinite cannot exist. He claims that it leads to mathematical paradoxes and problems. I am not sure what to think of this.

Also, is the premise that everything that begins to exist has a cause reallly demonstrated? It seems true from our intuition but this is not the same as being formally proven.

Lastly, does the big bang theory really say that the universe as such began to exist, from a previous point of non-existing? Or does it just say that at some point all the matter and energy in the universe was together in the form of a singularity?