Skins won't load on my server and I banned mobs from spawning but spawn eggs are?

I made a server for my school (I'm the T.A. In the class and we're using Minecraft to teach) Well, My friend and I were getting the server to finish the plots and our skins didn't load (I was Steve and my friend was Alex) We signed in and out a couple times to see if it was just a lag thing but it they wouldn't load. I didn't ban them or anthing so why aren't they loading?
Also I banned mobs from spawning but the spawn eggs work, but only for the monster spawn eggs, the animal spawn eggs don't work. Pic below is the server settings showing you I did ban mobs.Skins won t load on my server and I banned mobs from spawning but spawn eggs are

The image is extremely small, though you could do the following:

Check if your computers are connected to the internet. If you're using the school's internet, that might be the problem, since most schools are stingy over their firewall and ports.

As for the monster things, get a modded server tool. Not something like a forge server, but something closer to like Bukkit or Tekkit, where the host can ban items and other things. Then you ban all spawn eggs and set the world difficulty to peaceful. Peaceful prevents the spawning of all hostile mobs. It would still spawn neutral ones like cows, pigs, sheep, bunnies, etc but you can prevent those from spawning from editing the server files.

Because how I see it, the Minecraft games are loading as if they're not connected to the Mojang servers, which in turn prevent you from using your skins.