Do possible employers look at all the schools you've attended?

Employers absolutely look at where you went to school, as do graduate programs. Most often it's reputation in field that counts. For example, Harvard has a great law school, business school, and medical school, but it's not as well known for music. But the name alone sometimes does count for quite a bit, just because people can't always be bothered to know which school is better at what. Grad school admissions departments have actual multipliers that they put on GPAs from undergrad schools based on things like grade inflation, curriculum difficulty, etc, so if you go to an easy school known to have a high average GPA, and you get a 4.0, it might be only worth a 2.8 to the graduate admissions process. They have actual tables listing schools, programs, and multipliers to attach to GPAs. That level of detail isn't often followed by companies, though.

Most places don't care that much about high school. There are too many, with too wide variation, for a company to care. They might care about GPA, extracurriculars, etc, but once you graduate college it's best to not even put high school on your resume.

If getting an advanced degree is important for the field you want to go into, then I think it's more important to go to a well-recognized graduate school than a lesser known undergraduate school.