what about the improbability of the first living cell developing, surviving and reproducing, and the complex systems for life evolving by chance mutations? I've heard of the anthropic principle, but it seems to lead to the conclusion that the laws of probability are not laws at all, they just our human perception, and I can't accept that. And what about entropy? (order turns to disorder and decay with time and neglect).
You miss the point. Again.
There WAS no 'first living cell'. You are starting from a conclusion - that a cell is the goal, and what steps are needed to make it. That's not how evolution works. You can't think "I want a Picasso painting" and hand a kid a crayon and a piece of paper. Of course you won't get what you are looking for! If you hand him a crayon and a piece of paper and say "Let's see what turns out"....you are now thinking much more like what evolution does.
The problem is that creationists start with the assumption that humans - as we are now - are the pinnacle of perfection, created in gods image, and the ideal biological form. The first two assumptions obviously irrelevant - consider. ARE humans the ideal biological form? Of course not! We are but one 'form' that 'works' - can reproduce successfully and dominate our environment. We aren't even ideal at that - FAR too much in our environment can kill us (our immune systems do not protect us from everything on this planet, alone), several pieces of our anatomy don't belong, etc. We are, even now, a transitory species.
As to that 'first organism'.....the very FIRST organism would not be anything near as complicated as a cell. Indeed, it's likely cells didn't arise for several million years into evolution.
The FIRST 'living thing' relevant to this discussion would be a self-replicating ribozyme sequence. Akin to a virus, really. (And we can, by the way, see these spontanously created in experiements). Given the size of a self replicating ribozyme (very small) and the size of the area capable of making it (the 'protein soup' of the early Earth's mostly-ocean surface), it is likely many, many different kinds of self replicating ribozymes started. Some were not very successful (required too complicated an environment to succeed in replicating in, were too delicate, etc), and some were. Those that were, obviously, kept replicating with genetic variances introduced. Some of these were more successful than others, etc. Soon we would have protein coats forming on some of them - those would obviously be more protected and be more successful at reproducing than those without, and would soon dominate the early oceans.
BTW, as to how likely this is, TalkOrigins explains:
Quite good actually. There are 1.6 x 10^60 possible 100 nucleotide sequences. In a primordial ocean of 10^24 litres with a nucleotide concentration of 10^-6M (reasonably dilute), assembling a 100 nucleotides sequences on clay al la Ferris [3] and assuming it takes a week to make a full sequence, then you can have produced roughly 1 x 10^50 sequences in a year! As it has been estimated that one in every 1 x 10^17 random RNA sequences is a high efficiency ligase [4], the chances of getting at least one self-replicating polymerase (or small self replicating assembly) is quite high.
Survival should be quite good, polynucleotides are quite stable (in the order of thousands of years), and there are no competitions to gobble them up, so a replicating ribozyme should come to dominate any lake or ocean it is in. With competition for resources, variants of the original ribozyme will come to dominate in certain environments.
Anyway, these simple self-replicating molecules continue to reproduce, getting more and more complicated (or, more specifically, having variations in the genetic makeup that add complications, sometimes successfully, and sometimes not, with those that have added complexity and are more successful than the original form out-reproducing them and taking over the local population). Note that in all cases, 'success', is STRICTLY defined as the ability to reproduce better than it did before. A 'more successful' organism has nothing to do with being 'closer to what we consider life' or 'close to becoming sentient' - 'success' is merely gauged by how well it reproduces.
Eventually, the complexity reaches a point where something we would recognize as a 'living thing' is reproducing along.
TalkOrigins (again) summarizes the problem graphically:
Note that the real theory has a number of small steps, and in fact I've left out some steps (especially between the hypercycle-protobiont stage) for simplicity. Each step is associated with a small increase in organisation and complexity, and the chemicals slowly climb towards organism-hood, rather than making one big leap [4, 10, 15, 28].
Where the creationist idea that modern organisms form spontaneously comes from is not certain. The first modern abiogenesis formulation, the Oparin/Haldane hypothesis from the 20's, starts with simple proteins/proteinoids developing slowly into cells. Even the ideas circulating in the 1850's were not "spontaneous" theories. The nearest I can come to is Lamarck's original ideas from 1803! [8]
Given that the creationists are criticising a theory over 150 years out of date, and held by no modern evolutionary biologist, why go further?
Check out their site - it's a fountain of good information!