To the first one, Big Bang theory doesn't hold that at first there was nothing. Leading belief says that it started with an enormous... well, everything. A great big ball consisting of all the matter in existence. For some reason, it exploded, and thus, the Big Bang.
Me agrees and disagrees. Theists hold that there is no such thing as necessary existence, except God. Atheists/Agnostics/what ave you hold this universe can necessarily exist. If it is number one, then its trouble for the atheist, since the atheist/agnostic has to prove how can being (be it quantum vacuum, thats still something) pop out into non-being, because that kinda goes against Causality. If however this universe exists necessarily, then as far as we can trace back to is the quantum vacuum, thanks to Professor Hawkings (and others of course). This is basically the crux of the matter.
As for the oscilating model i.e. an infinite number of universe existed before this very one and the bang-crunch-bang-crunch thing, well thats been criticized. Entropy kinda rains on its parade. A new big bang would require energy, but with every succession of universe(s), there would be increase in entropy, since this universe is an irreversible process. So infinity doesnt account for it, since at one point the universe would reach a state where there is no more useful energy for another bang. So we cannot agree with the oscillating model.
Plus, the universe being infinite in time would suffer philosophical critic too, since infinity cannot exist in reality.
As for the second, no one knows for certain, but consider that organic life boils down to carbon-based chemical compounds arranged in a complex structure. It only had to react once, in one place in the world, and then asexual reproduction takes over, evolution begins, fast forward about 3.5 billion years and we're here, fully evolved sentient discussing how it all started. Poetic, n'est pas?
The criticism that I have against abiogenesis is not that its improbable, but its impossible. Many scientific facts severly critique this hypothesis. Lemme link you to the following paper:
It (among other things) discusses the issue of the troubles abiogenesis faces. The first cell to have been borne out of dead matter has many intellectual stumbles to it. By the way, its not just panspermia. It doesnt only go against the empirical observation of the early environment of this earth, it goes against the basics of Chemistry and Biology on many levels. So the only way you would think this is plausible is if you could enter a whole new set of laws from somewhere else.