If I'm on an open wireless network, can a 3rd party capture packets and see all the internet traffic to and from my computer? What if WPA encryption is used, but someone has the key already? If I use HTTPS, can someone with direct access to the router decrypt the traffic and view it somehow?
Yes
Same as if the network was un-encrypted
Unlikely. They would need to have both the Private Key and the Public Key for your HTTPS host, which is unlikely. The other possibility is what's called a "man in the middle" attack, where they replace the certificates with ones that they know, so that it appears to be encrypted, but the man-in-the-middle does a translation on your HTTPS traffic so that it can read it.
Short answer: If you're on a wifi network, don't do anything you don't want to be made public.
If someone is on the same wireless network as you or you are on an open network they can see your raw traffic. Now if that traffic is encrypted, for example with HTTPS, then they can only see the encrypted traffic. As far as I know there is no easy way to decrypt HTTPS traffic.
HTTPS is between your browser and the webserver, so that traffic is encrypted, though someone can capture the packets and try to break the encryption.
Given enough motive, just about any wifi encryption can be broken. You can see the traffic using some freely available tools as it is broadcast out, but someone would need to separate out what is meant for you and someone else. The wifi adapter can determine that, so programs exist to determine that.
How secure your wifi is is based on how strong and secure your key is and the encryption algorithm.
Here is an article about wifi security, and you can google and get more info on various encryption algorithms, such as WPA, and see how secure they are.
http://pogue.blogs.nytimes.com/2007/01/04/04pogue-email/
To sniff the actual traffic traversing a wireless network requires a wireless adapter and driver that support RF monitor mode, which few adapters in the retail market do. Adapters of these type are usually found in the wireless testing and engineering industries and are usually cost prohibitive for the average user.
While it's true that a determined hacker will eventually circumvent just about any security mechanism, I wouldn't count on the average Joe being able to do this. That being said, I don't recommend using publicly available open wireless networks.