Spamming drills is never, I repeat, NEVER a good idea. You WILL get read and punished if you get happy doing this. That being said, Eddie is not a character I would recommend for newer players (this should not discourage you from learning him however) mostly due to his steep learning curve and momentum based gameplay.
As for normals? His aren't great for much, however, 6P and 2HS are your main anti airs, but they can be unreliable. 6HS can be used as well, but that is even more unreliable. His farthest ranged ground normal is 5HS although it's unsafe as all hell.
A basic blockstring (w/o the shadow) would be: 2P, 5S, 2S, 22S. You can however opt for another 5S into 22HS.
BnB's are a bit more difficult however. Are you familiar with how the shadow works?