There's no map, but they do have hacks that will show you the whole map. I don't like to use them because they won't just show you what you've explored. They'll show everything. Like where the jungle is, sky cities, corruption, ore, treasure chests, everything.
Here's the one I've used before. It's helpful if you are starting to get bored, but half the fun with this game is finding things out on your own. It's compatible with the latest patch.
I'd use medium. Large is really large. Best used with multiplayer. Small is a little too small. You'll find good ore way too quickly and not as many cool areas to explore. Medium is what I always choose. I've been tempted to try large, but seriously medium is pretty big.
I'm not sure about difficulty being affected, but having a huge area will be pretty hard getting around in the game. It'll take forever and a day to get to the ocean.
From Terrariaonline Wiki: Getting Started
Small worlds are compact. The oceans are much closer to the starting point, and the entire world is not as deep. The Corruption is only in one or two places.
Medium worlds are well proportioned. Traveling to the edges will take roughly a day of time, depending on how well the character is equipped. The Corruption is in two or three places.
Large worlds are massive. To reach the deepest sections of the map will take quite a while, and the oceans are easily days apart. The Corruption is in three to four places.
It used to be faster if you set it to "frameskip", but it did make the enemies quicker as well. Still would have prefered if it was a bit faster. With better picks you'll mine faster. I have a silver one right now and it's a definite improvement. Same goes with axes and hammers. The better quality the faster you go.
You have to have a entry point three blocks high to place a door. No more, no less and put the door in your hotkeys then place it by clicking near the top of where you want to place the door. It should place it then.
Something like this: * = wood(or whatever you are using) + = empty space
Put the door on the top +
*
*
+
+
+
*
For wooden walls you use an axe instead of a pick to remove them. I make that mistake a few times when finding wooden houses underground. If I haven't played in a while it'll take a second to remember that I need to use an axe.