Short answers, pulled from the story.
The Mendelian gene is the basic unit of heredity, the classical gene of genetics that refers to any heritable trait. The molecular gene is a sequence of nucleotides in DNA that is transcribed to produce RNA, and it is the definition used across biochemistry, molecular biology, and most of genetics.
Gregor Mendel discovered the existence of discrete heritable units while studying 8000 common edible pea plants in Brno from 1857 to 1864, though he did not use the word gene. Wilhelm Johannsen introduced the term gene in 1909, from the Greek gonos meaning offspring and procreation.
The number of protein-coding genes in the human genome is estimated at about 19,000 through the ongoing GENCODE annotation project, down from earlier estimates of about 30,000. The latest estimates from Ensembl suggest about 26,000 noncoding genes.
The two types of molecular genes are protein-coding genes and non-coding genes. Non-coding genes produce functional RNA molecules such as ribosomal RNA and transfer RNA, while protein-coding genes are transcribed into messenger RNA that is then translated into protein.
Gene expression requires two steps: the gene's DNA is first transcribed into messenger RNA, and that mRNA is then translated into protein. RNA-coding genes go through the first step but are not translated, since the RNA molecules are themselves the functional products.
Genetic engineering is the modification of an organism's genome through biotechnology, with techniques to add, remove, and edit genes developed since the 1970s. Newer methods use engineered nuclease enzymes to create targeted DNA repair, and gene therapy can edit the genomes of cells in an adult organism to treat genetic diseases.
Only a small portion of an organism's genes are essential. Escherichia coli and Bacillus subtilis have an estimated 250 to 400 essential genes, the yeast Saccharomyces cerevisiae has about 1000, and mice and humans are estimated to have around 2000 essential genes.