Because it’s selected for, at least recursively based on entity specific attractors. In this case bacteria, another case mating preference.

After the first few generations of the gene, sure. But the first organism to get it probably got it somatically and transferred it through gametes.

Evolution is hill climbing, but the gene introduction was random. Just as mutations themselves are.

I don’t think it’s purely random like what random actually means. It’s a set (or graph if you wish) with bias. All biology has a bias.