Feel free to check the other parts of this series for other traditions that we observe in the dojo.
We don't wear shoes on the training floor in the dojo. There are many reasons for this. Part of it is simple tradition. Many karate-ka of the past did not wear/own shoes. It is also the Japanese/Okinawan tradition of taking off shoes when entering a home. This is done for cleanliness as well. Training barefoot also carries practical benefits. Training barefoot toughens up the parts of your feet that you will use for kicking techniques, and improves your balance.
We line up in formation according to belt rank. This tradition was actually borrowed from the French Military. The Okinawans saw this and realized the benefits. It organizes students according to their level of knowledge which is useful in running a class. It also has the less experienced students standing behind more experienced karate-ka so that they can look at the more experienced peers to see what they should be doing/how they should be doing it.
When joining/rejoining the formation, we never cut in front of other students (especially if they are a higher rank). This is a sign of respect and value of the training of others. You wouldn't want someone to stand in your way when you are trying to see something your Sensei is teaching you.