Does all the Carbon on earth come from dead stars?

One proton and one electron came together to form the most fundamental atom in the universe, hydrogen; all other elements were formed by star fusion reactions, where two hydrogen atoms smashed into one helium atom, which then smashed into two more times to produce three protons total, creating lithium, and so on. This process produced the majority, if not all, of the carbon in the universe.

Since carbon atoms have six protons, the following fusion reactions can produce carbon: boron (five protons) to hydrogen (1 proton), beryllium (four protons) to helium (two protons), and lithium to lithium (three protons).

The exploding or "nova" state of stars releases those elements into space.

The other process by which elements are formed is through radioactive decay. The most well-known radioactive element is probably uranium, which decays into a variety of elements until it eventually decays into a stable state of lead.

Another way that an element can be created is by a process that could be called substitution (thanks to @Olthe3rd for providing this information). This process involves an energetic particle striking an atom and dislodging a proton. For example, to create carbon-14, the radioactive form of carbon that is roughly one trillionth of all carbon on Earth, a neutron strikes a nitrogen atom (7 protons) and dislodges a proton (while leaving the neutron affixed). The result is a radioactive carbon that decays back to nitrogen.

No, not all carbon on Earth originates from dead stars. Sure, a big amount of carbon is created in stars by nuclear fusion reactions and gets released into space by supernova explosions, but some carbon is also formed by other processes like reactions in interstellar dust and cosmic ray spallation.