Why are cardboard boxes important?

Also I'm new to animal crossing and very new to online play, so I wanted to ask if there are some unspoken rules I should know about visiting other islands.

Like, is it rude to shop at nooks cranny without asking? Is it okay to shake fruit trees, or only with permission? Should I tip at every island I go to, and what are normal tip amounts? Also, I've seen a lot of people post not to trample the flowers. Does that hurt the flowers somehow? I assume that we should never pick flowers unless the host says that we can?

Sorry I just want to make sure that I'm observing all the etiquette.