Does all the Carbon on earth come from dead stars?
Most, if not all, the Carbon in the Universe, not just on Earth, came from dead stars.
In the formation of the Universe, the most basic of atoms, Hydrogen, was made with the coming together of a single proton and a single electron. The formation of all the other elements were made in the fusion reactions of stars: 2 Hydrogen atoms smashing into each other so hard that they fused into 1 Helium atom, and then smashed again to have 3 protons in total and so making Lithium, and so on. This is how most if not all of the carbon in the Universe was made.
Carbon atoms have 6 protons. The fusion reactions that can make carbon are: Lithium to Lithium (both have 3 protons), Beryllium (4 protons) to Helium (2 protons), and Boron (5 protons) to Hydrogen (1 proton).
Those elements are released into the Universe through stars exploding, or going nova.
The other way that elements are created is through radioactive decay. Probably the most famous of the radioactive elements is uranium. A single atom of uranium, when decaying, will transform into many different elements until ultimately it decays to a stable state of lead.
There is yet another way that an element can be created and it's through what might be called substitution (thanks to @Olthe3rd for adding in this piece of information). It's process where an energetic particle hits an atom and knocks a proton loose. In the creation of Carbon 14 - the very famous version of Carbon that is used to date fossils and things, a Nitrogen atom (7 protons) is hit by a neutron, dislodging a proton (and the neutron stays affixed). Carbon 14 is radioactive and decays back to Nitrogen. Carbon 14 makes up roughly 1 trillionth of all the Carbon on Earth.