Short answers, pulled from the story.
Gregor Mendel studied inheritance patterns in 8000 common edible pea plants within the garden of an Augustinian monastery in Brno, Austrian Empire. He tracked distinct traits from parent to offspring and described these mathematically as 2n combinations where n is the number of differing characteristics in the original peas.
Experiments showing that deoxyribonucleic acid DNA was the molecular repository of genetic information were conducted during the 1940s to 1950s. James D. Watson and Francis Crick published a model of the double-stranded DNA molecule whose paired nucleotide bases indicated a compelling hypothesis for the mechanism of genetic replication.
In 1965, the lab of Max Birnstiel was the first to isolate single genes which were ribosomal RNA genes from Xenopus laevis. Walter Fiers and his team determined the sequence of a gene in 1972 which was that of bacteriophage MS2 coat protein.
In bacteria, an estimated 250-400 genes are essential for Escherichia coli and Bacillus subtilis which is less than 10% of their genes. Half of these genes are orthologs in both organisms and are largely involved in protein synthesis.
Typical mammalian protein-coding genes are about 62,000 base pairs in length transcribed region and since there are about 20,000 of them they occupy about 35-40% of the mammalian genome including the human genome. Eukaryotic genes often have introns that are much larger than their exons and those introns can even have other genes nested inside them.