Character interaction covers a wide range of things. There is only one character that actually speaks to you (of those wearing a suit) and that is Mickey in Town Square in the Magic Kingdom. And while he is really cool, he’s not actually responding directly to things you say - he is using preprogrammed phrases to interact. I think. All other characters in a suit interact with gestures and many of those do give autographs and take pictures. They do a great job of getting their point across without speaking. Face characters, such as princesses and such, do talk to you, along with taking pictures. I hope that’s clear - it’s hard to explain!
And yes, while years ago I hear that characters just wandered, it happens less now and is much more “scheduled.” I wouldn’t rule out seeing an unexpected character here and there, but I wouldn’t expect it either.