Question: Why was Beethoven arrested? He wasn't doing anything illegal.
Question: Why does Rufus send Bill and Ted off on their own, instead of going with them and helping them?
Answer: The adventure wasn't just about helping Bill and Ted with their essay. It was also about helping Bill and Ted achieve independence, which would later contribute to their reputations in the future. If Rufus just told them exactly what to do, they likely wouldn't have learned to achieve their independence in the same way. They needed to learn it for themselves.
Answer: While it's not unusual for musicians to try out new instruments (playing a few rifts and even entire compositions) in a music shop, Beethoven's extended sampling-keyboard performance went wild, drawing an enthusiastic mall crowd into the relatively small music shop. The shop manager no doubt felt overwhelmed and called in mall security to clear out the shop before any damage and/or theft occurred. Keep in mind that the security team was already scrambling to respond to several simultaneous disturbances throughout the mall, all caused by 7 strangely-dressed oddballs (more than half of whom only spoke obsolete dialects and ancient languages). The time-travelers were, thus, probably all perceived as one group of pranksters or escapees from a mental institution.
Charles Austin Miller