Welcome to the forums, Ebiru!
1) A good place to get songs is the simfile section on Zenius-i-Vanisher
. They have a huge variety of official DDR songs and fan made songs which cover a wide range of difficulties. You can also check out this post I made
detailing several beginner-friendly song packs to get you started.
2) No idea. I believe it's possible to play online with others but it doesn't work very well. You can try checking out Stepmania Online
for more info.
3) Well, they start at 1 and get harder as the number goes up! :P
Seriously though, each difficulty has a number associated with it. The numbers are the same across difficulties - e.g. a medium level 5 would be about as hard as a hard level 5 or easy level 5, not particularly easier or harder. You can see the difficulty levels when you pick a song - I've circled them in the picture at the bottom.