Well for your first question, many maps in LM doesn't have a portal that goes back to the map you came from. The blue dots are portals and the one in Xmas is hidden in the big present (you stand underneath the present and jump up), which leads to Default. Like RakshaW pointed out, the easiest way to escape a map is to just go home by typing in the chat or opening the home box by pressing H and then clicking go home.
Your second question, I don't know what could be wrong with your weasel and deer, I've played with both models and they work fine. Have you restarted the game and then logged in with your weasel/deer again? Some people say resizing characters helps, I think.
Third question, try changing your rendering system and play your game in windowed mode if you don't already. This might help with the lag.
