I’ve been a staunch proponent of evolution since a very young age. I’ve never questioned the theory, which was in my heart a law. Proof was never essential, but lately… I seam so doubtful.

Question

Here are just a few things I have problem believing:
1. The change of abiotic matter (non-living) to biotic matter (living).
3. How probability favours natural selection.
4. The change of unicellular organisms to multicellular organisms.
5. The idea that our biological being strives toward perfection.

I don't know any scientific basis for the last. I don't know that biological beings strive for anything: they do things, such as reproduce, consume food, etc. If that is turns out to be of reproductive advantage, they grow in number. I don't know if you classify that as striving. Perfection? That is in the eyes of the beholder. Number 5 is not scientific language.
Random mutations with some reproductive advantage popping up can explain number 4. Probability favoring natural selection? Hmmmm. For every mutation, it will have some related survival and reproduction factor. If that factor is large enough, as compared to other mutated organisms, then it will by the laws of population genetics, have a reproduction advantage. Yes, there is a lot of probability and statistics modeling in population genetics. There are good basic books on that.
Finally, number one: I don't view the change as dramatic as you proposed. The changes are gradual, and the dividing line between fuzzy. Living and non living are our definitions, not the network of molecules in the matter.
Remember, the great majority of mutations in organic molecules are dead end. In living matter as we know it, these dead end mutations are removed by the organism itself.
You seem to have some emotional involvement with this subject (words such as heart, doubt, being, strives,doubt, perfection). If you attach feeling or emotion to biochemistry and its alterations, your view will be tinted by the window through which you look.
There are good basic books on this, however, the subject is of great importance to some with fixed religious or philosophical views, and those books are tinted with their window they look thru. It is hard to see clearly in a storm of controversy. Avoid that.
Good luck.

Well said!