First advice - don't use homegroup at all, rather classic sharing method.
Wireless is well more than enough to stream any type of music format there is. Even uncompressed DVDs and Blu-Ray!
Speed should not even be a concern. If it is, something is wrong. We could perhaps configure the router and/or adapters better.
I don't know about syncing Office but knowing Microsoft and their corporate customers, this is definitely something they'd want. So 99% sure it would be possible.
Let us know if/when you would like help with any of that. It may be a little bit of a process for you to undertake but once it is all setup correct, you will be very glad about it. Set it and forget it as I say.