Yes, we are unable to hear any of the candidates' arguments when they are arguing with interruptions. It is also highly impolite to interrupt anyone who is speaking. What message are they sending us when we see them acting like no other side is important but their own? Are they going to fight only for themselves after the elections?
The mark of a good president is not who can do more interrupting during a debate. We want to hear what each candidate has to say. The candidates know the rules going into the debate and they should be prepared to follow them. A person who interrupts should lose time in the future to make it fair.
Yes, there should be punishments for interruptions during debates. Rules are set up and agreed upon before the debates. Both candidates agree to abide by the rules such as time limits and interruptions. If a candidate does not adhere to the rules for any reason, they should be penalized or at the very least called out for the violation.
If the crowd, as a whole, erupts in applause but quickly quiets back down, then there should be no penalty. The debates prove to be extremely emotional and people are severely invested in the future of our country. If, however, a singular person or group calls out, banters, or badgers the candidates, there should be a penalty for such an instance.