In the US and Canada in the 1800s, there was a lot of land on the western sides of those countries that was unowned according to the governments of those countries.* Those governments allowed people to move from cities on the eastern side and "stake a claim." (Mark an area of land - sometimes by putting sticks ("stakes") into the ground - and then register it with a government office.) Then if those people followed certain rules (usually live or farm there for a certain amount of time), they would get to own the land.
"Staking a claim" means that the person started down that path toward land ownership.
b) a "switch" is a branch of a tree that you have selected to hit someone with (usually as a form of punishment). "Take a switch to you" means "I'll hit you."
c) before we understood how planets and stars and galaxies (&tc.) work, some people had the theory that the earth moves through a substance called "ether." (It doesn't.) "ether" is still used poetically as a synonym for air or a synonym for space.
d) when a person is "enheartened" it means that they have a very strong, positive feeling to do something. (Good feelings come from your heart.)
e) A "commencement" is the graduation ceremony (usually for a high school or college). "Commencement" means beginning - and graduation is when you begin your post school life. (The ceremony at the beginning of school is often called "convocation.") A "commencement address" is a speech that someone makes during that ceremony.
f) "from scratch"
means from nothing. If you start "from scratch," it means you have very little or money or supplies. If you cook "from scratch" it means that you start with eggs, flour, raw vegetables, etc. instead of using a mix or something that is already somewhat prepared.
* There were people who lived on and used the land. The governments ignored them.