Short answers, pulled from the story.
An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. More than 99.94% of an atom's mass sits in the nucleus. In the Standard Model, protons and neutrons are themselves composed of quarks, while electrons are elementary particles with no internal structure.
The number of protons in an atom, called its atomic number, distinguishes each chemical element from every other. Any atom with 11 protons is sodium, and any atom with 29 protons is copper. Atoms with the same proton count but different neutron counts are isotopes of the same element.
J. J. Thomson discovered the electron in 1897 when he found that cathode rays could be deflected by electric and magnetic fields. Between 1908 and 1913, Ernest Rutherford, with Hans Geiger and Ernest Marsden, discovered the nucleus by firing alpha particles at thin metal foils and observing some deflect by angles greater than 90 degrees.
Ernest Rutherford named the proton in 1920 after concluding in 1919 that alpha particles splitting nitrogen nuclei released hydrogen nuclei. James Chadwick discovered the neutron in 1932 by exposing elements to beryllium radiation and measuring the recoiling particles to find they were neutral with a mass close to the proton's.
Atoms are typically around 100 picometers across, and a human hair is about a million carbon atoms wide. They are smaller than the shortest wavelength of visible light, so they cannot be seen with conventional optical microscopes, though individual atoms can be observed with a scanning tunneling microscope.
Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in about three minutes but no carbon or heavier elements. Carbon up to iron formed in stars through nuclear fusion, while elements heavier than iron formed in supernovae and colliding neutron stars through the r-process and in AGB stars through the s-process.