I'll try my best at this although I've only been involved with OpenSCAP some time ago doing a bit of integration with libguestfs ...
> 1) what types of things does OpenSCAP audit?
It uses a big XML file of tests (which generally you don't write - that is supplied by the OS vendor), called OVAL files. The tests can do a lot of stuff, I believe arbitrary stuff, but in general it's things like checking the permissions of files and directories, checking versions of packages installed to see if they are vulnerable, looking for misconfiguration, and so on.
> 2) does it support my mixture of operating systems?
Well you need the vulnerability data - ie. the XML/OVAL files. Red Hat [the company I work for] supply this for all of our Red Hat Enterprise Linux systems, and I believe you can get it for Windows too, but I don't know about others.
Here are the RHEL files: https://www.redhat.com/security/data/oval/
> 3) is it for scanning remotely over a network?
> 4) does it scan the configuration of a computer from a local daemon?
It's running a process inside the machine under test (and hence it's not really good for testing machines which have already been compromised and where the compromise has countermeasures). You can automate the program in the usual ways which would allow you to initiate a scan from your puppetmaster / ansible / whatever.
One of the things I did was extend it so that you can examine a disk image using libguestfs, but unfortunately only a subset of tests is then able to run, basically only those tests that can be done through pure file access. Nevertheless this allows you to scan (eg) all your VMs to see which ones are vulnerable to some subset of problems.