1) I don't put custom skins on my server, so I can't say I have
2) The one that might be imporant to you, client-side, is cg_deferPlayers "1". That setting makes you wait until a map load or you hit "tab" to bring up the scores before it will load a model a player is using who entered the server after you.
3) Yes, a client must have the skin installed to see it. If they don't have it installed, they'll see anyone using it in a default skin instead.
"Do you expect me to talk?"
"No, Mr. Bond, I expect you to DIE."