who discovered this part of the cell?
Richard Altmann
Mitochondrion
The first observations of intracellular structures that probably represented mitochondria were published in the 1840s. Richard Altmann, in 1890, established them as cell organelles and called them "bioblasts". 
which of these processes takes place in the mitochondria of a cell They supply cellular energy, and control the cell cycle and cell growth.
wiki:25646192
Mitochondrion [SEP] History of discovery and research
The first observations of intracellular structures that probably represented mitochondria were published in the 1840s. Richard Altmann, in 1890, established them as cell organelles and called them "bioblasts". The term "mitochondria" was coined by Carl Benda in 1898. Leonor Michaelis discovered that Janus green can be used as a supravital stain for mitochondria in 1900. In 1904, Friedrich Meves, made the first recorded observation of mitochondria in plants in cells of the white waterlily, "Nymphaea alba" and in 1908, along with Claudius Regaud, suggested that they contain proteins and lipids. Benjamin F. Kingsbury, in 1912, first related them with cell respiration, but almost exclusively based on morphological observations.