@Zachary DuBois, it depends on your settings on the General Settings tab under Miscellaneous. If you check Hide perf settings then only the network admin can change the setting on a per site basis. If you select use single network conf only the settings set under network admin are used and there are no per site settings.
If I edit only the network settings for W3 Total Cache and enable caching, will it be enabled and run on all sub-sites?
Only if you check Apply to network.
If I am using S3 and CloudFront, will it work using the same bucket if it does need to be configured for each site?
If names of files or path to files differ should be able to use same.
If the network settings work for all sub-sites, can I use S3 and CloudFront (Same bucket)?
If names of files or path to files differ should be able to use same.
Does this work with a subdomain instal using WPMU Domain Mapping?
Domain mapping is supported.
What settings do you recommend for using this with BuddyPress and bbPress?
Using default settings would work fine. The activity listing page for non logged in user if that is used with BP might need to be excluded from cache if you want it up to date. Also listing of online users might need to be handled as well. Might need to use custom code for handling that. Check page fragment caching in the FAQ.