If I am running Windows 7 and change the default ciphers on the PC, does this affect the connection between the client and server? If a similar change is only made on the server, does it affect the client? What if the changes are made on both the client and server?
Yes. Client and server negotiate to pick which cipher will be used in an SSL/TLS session. So you could on your server or client and disable all the CBC ciphers and get rid of your exposure to BEAST. Most likely the best choices for ciphers are RC4 and 3DES though 3DES would be in CBC mode so not until MS fixes their implementation per discussions a few years ago. You should probably also check the root list on your client to make sure you don't by default trust every government and business in the world to manage your trust decisions for you.