Definitely interrupting, and on that note the people that start talking right when you finish are kind of annoying too, because you know they probably didn't listen to you anyway and were thinking about what they wanted to say while waiting for you to finish.
I check my voicemails about once a month no matter how many I have, or when they max out around 13 or 14. Mostly it's just job recruiters and I'm not particularly looking. My parents figured out after a couple years that I don't check them often, so if I don't answer they send me a text or call the wife. Sometimes they just skip the trouble and call the wife first at this point. I do answer when they call and I notice it though, just have my phone on silent. I don't have any friends that call anymore, unless they're hammered, and even that has pretty much slowed down now that they can just send me a snap. Also, I deleted Fb, so that's nice.
I respond to texts quickly or when I wake up and emails at least within a few days depending on how important it is, might respond same day.