They are playing with marionette puppets in zero gravity. The people are floating yet the puppets are hanging on strings, even when they are tugged. The puppets should be floating as well and when tugged should float away.
During the video call immediately after the puppet show, when Misha is in an emotional state, his tears are seen falling downward as if affected by gravity. However, the call takes place in the zero-G section of the Atlas, meaning that in reality, the tears would pool together into a floating blob, not unlike the vodka shots seen towards the end of the episode.
The communication delay is finally addressed, with a character noting that halfway into the 8 month voyage (which would actually take a little over 3 months given the known distance and stated speed of the ship) voice and video would no longer work, but they could still send texts and emails. The character says eventually a text could take an hour or more.
Mars is about 39.9 million miles from Earth, and 39.7 million miles from the moon. By the time the ship had traveled 2 months at 17,500 MPH, it would be over 25 million miles from Earth. Since radio waves travel at 186,000 miles per second (or 11,160,000 miles per minute), it would take about 2.2 minutes for a message to be received, and of course another 2.2 minutes for the response to be received. Even at the full distance of 39.9 million miles, it would only take about 3.5 minutes for a message to be received, not an hour or more.
Mars is about 39.9 million miles from Earth, and 39.7 million miles from the moon. By the time the ship had traveled 2 months at 17,500 MPH, it would be over 25 million miles from Earth. Since radio waves travel at 186,000 miles per second (or 11,160,000 miles per minute), it would take about 2.2 minutes for a message to be received, and of course another 2.2 minutes for the response to be received. Even at the full distance of 39.9 million miles, it would only take about 3.5 minutes for a message to be received, not an hour or more.