Good Riddles

Question: What goes up with the intention of falling down?

Question: I'm not a pool, a tree, a slave, a website, or a shirt.

What am I?

Question: My eye is dark,
and my mane is yellow.
You man see me at the mart,
and I'm probably taller than you fellow.

What am I?

Question: Not chest or box is now discussed. Money can be held in it, but just as we test its metal, within it there is rust.

[What is it?]

Question: You can call me a home, but I have no doors.
Someone lives inside me, but leaves when there's no more.

What am I?