Thanks for the question:
"To maintain or improve our rankings i'm looking for specific information for the link structure. For example, is it better to have the 'about us'/rel=author on each domain, with contributors on that specific domain or is it better to have them all in the (umbrella) brand domain."
I'd say that it comes down to how much you want to differentiate your current brands from each other. If you want to keep them quite distinct and each one has it's own team / writers / USPs etc, then you are best to have each domain have it's own sections.
"I think to maintain the rankings it is best to keep specific content (like blog/ about us) on the domain. So is it the best to just do side wide links with a logo (like health.com) and what about hosting? We work with wordpress, so all domains will be hosted on one ip? when we use the multiple site option of WP?"
In terms of cross-linking, I'd say that you should try to do this where relevant and as James has pointed out below, as long as you're not doing this in huge volumes, you should be fine and not trigger any problems with Google. The only time you may want to be careful is where your domains are competing for the same types of keywords. I would avoid cross-linking too much with exact match keywords as this could be seen as manipulate, I'd keep it on brand and to relevant pages.
If the domains you own are in the same niches, then you may hit problems of them competing against each other. I'm not sure if this is the case? If they are in the same niche, then Google certainly can look at things like IP address and footprints that links the sites together, it is hard to know to what extent this would harm you but Google certainly prefer to show diversity in search results rather than having multiple sites from the same company.