Present a BETTER worldview

[Welsh cake]

- please present a BETTER explanation for the existence of our universe, a cosmological argument, which is more rational than Theism gives us. Why is there something, rather than nothing?

Here's the PREVAILING cosmological explanation of the universe's early development:

Big Bang

- please present a BETTER explanation for the fine-tuning of - The over 120 finely tuned constants of physics to permit life on earth

120? So needless to say you've already done the research required and are simply disappointed God's not one of them?

At any rate a secondary education level science textbook that covers the basics to organic reactions is all you need to understanding the fundamentals involved in biochemistry, if you're referring to Abiogenesis (quite possibly owing to your vague OP) I recommend you give this site a visit:-

http://www.talkorigins.org/

- The initial conditions of the universe. how was it possible the inflation rate of the Big Bang being finely tuned to degree of 1 of 10^120 ?

We can't. That still remains one of the unsolved theoretical problems in physics:

Cosmic inflation

- the galaxy- sun-earth-moon system :

Nebular hypothesis

considering :
to have just one life permitting universe, you need 1 to 10^500 attempts to get it done.

This... is nonsensical. What do you mean by "x number of attempts" exactly? By life permitting universe I'm assuming you mean the potential for life in the universe? Regardless of how improbable it is?

Beside this, the Multiverse argument does not explain away God.

Oh please, these are hypotheses in physics, they have nothing to do with personal belief in magic man in any case.

Jupiter attracts all asteroids , avoiding these to fall to the earth, and make life impossible.

Sorry, but your assertion is broad-faced.

-please explain a BETTER mechanism than design for DNA, consciousness, the hability of thinking and speech, and morality.

Please phrase the question in a form that is sensible and legitimate.

-please explain, what meaning your life has. And if it has no reason, how can you live happy knowing, that your life is completely futile and senseless ?

I give myself a meaning, a purpose, that's how.

Oh dear I've gone and made your god-concept even more useless than it already is haven't I?