Short answers, pulled from the story.
The Second Triumvirate began on the 27th of November 43 BC when the lex Titia transformed Mark Antony, Lepidus, and Octavian into rulers with absolute authority. This law allowed them to make or repeal legislation without senate approval and issue judicial punishments without due process.
Ancient records provide varying figures for the number of proscribed senators including Livy who mentioned 130 senators and Florus who gave 140 senators. Appian described a list starting with 17 names followed by two rounds adding 130 and 150 others while Plutarch recorded figures ranging from 200 to 300 men.
Brutus and Cassius reached Philippi in early September 42 BC where Antony constructed earthworks on Cassius' flank to force battle despite weak supply situations. Cassius died by suicide after his camp fell to Antony and three weeks later on the 23rd of October 42 BC Brutus offered battle again before dying by suicide following defeat.
Relations deteriorated when Sextus Pompey raided Italian coasts and Antony sailed to Brundisium where Octavian's garrison refused admission leading to siege conditions. The situation worsened further when Antony divorced Octavia choosing to stay with Cleopatra which alienated Italian public opinion.
The Second Triumvirate ended with the victory at Philippi according to Tacitus though the final collapse occurred after the sea battle on the 2nd of September 31 BC at Actium. Octavian took Alexandria on the 1st of August 30 BC killing Caesarion and Antyllus while capturing Cleopatra's children to conclude the conflict.