Can my racket go over the net, and what if I touch it?

Under Law 13.4 it is a fault, while the shuttle is in play, if you:

• touch the net or its supports with your racket, body or clothing
• reach over the net into your opponent's court with your racket or body. The one exception: you may follow through over the net after hitting the shuttle, provided the first point of contact was on your side
• go under the net into your opponent's court so that you obstruct or distract them
• obstruct an opponent from making a legal stroke when the shuttle is following through over the net
• deliberately distract an opponent, for example by shouting or gesturing

So you must hit the shuttle on your side of the net, but your racket may carry on over it after the hit.