I'm no lover of orthodox theories but let's deconstruct the claims...

"Galaxy HUDF-JD2 (red dot, center) is so far (13 Billion lightyears) but has 600 Billion sun masses (4 times our own galaxy) and this is physically impossible."

*** I don't know why it's impossible (too big too young) but I'd 1st validate the asserted mass and get additional examples before tubing the BB theory.

"Another issue are the dark energy and the dark matter...Convenient for the Big Bang theory but so much of them are needed and so little detected"

*** So what if much 'dark matter' is needed by the theory? Au conrtarie, Dark matter IS detected, well established via gravitational influence in spiral galaxy rotation rates and in gravitational lensing by galactic clusters indicating a much higher mass than the ordinary matter produces. And dark energy has a well observed (by several different groups) effect on the expansion of the universe.

"breaches are appearing in the Big Bang theory. Theorists are not panicking yet but are on the verge of it."

*** I question this assertion. Would that it were so, since we'd find out something wicked neat that we've missed.

"And the Big Bang theory also rests on 2 unmatchable theories: general relativity and quantum mechanics."

*** That's a problem endemic to our lack of understanding of physics, not the BB theory.

Current cosmology is at a dead end.

*** I see it as being at an incredibly rich and evolving state. Your mileage may vary.

Some are questioning the fundamental constants (speed of light constant, gavity law constant?).

*** This is good, not bad. So far all the variable constant theories have failed any experimental test. Maybe one will succeed and we'll have to tweak or supercede our current theories.

"And what about results from Wmap?"

*** I dunno. What about them?

In any case, science just tries to put out for display and critique the best known 'approximation' of reality in its laws and theories. None of them are final solutions. Works in progress that work to the limits of experimental evidence until a better approximation comes along.

Maybe this universe was always there, but I see very little substantive evidence that indicates that that is believable. I do see lots of evidence of an evolving universe that started out very hot.