#1 reasonably high? We turn down plenty of Stanford grads. What's their GitHub like?
#2 degree basically never comes up, except if someone is saying they had an atypical degree path. And institution? Never, unless it's a part of someone's identity and they are a big "I am a college team guy"
Test 1: If a resume showed up from Stanford CS, how likely would it be that you or your coworkers would completely ignore it without giving them a call?
Test 2: if you had an employee with Stanford CS how likely would it be that your coworkers would ever mention that individual having that degree?