Yes to all. But I have to say almost no person on the street, let alone on the streets of China, probably heard of Bates. Amhearst, probably. And no person on the street outside CA probably heard of Pomona, arguably the best liberal arts college imo.
Brand names is almost solely due to colleges having a lot of money or athletic success.
You must be a genius being able to get 5s in 8 APs by studying on your own for 14 days. My kid took AP Arts History class, and all they did was study for AP test, and he only got a 4. And he got into Stanford early. Just goes to show you the smartest kids are not at HYPSM. I am impressed if what you say is true. You didn’t even take any AP classes? If true, you should have no problem acing LSAT.