You would be far better served setting up a workgroup for this type of mixed network. What you are seeing in the picture you posted is that the name of your Workgroup is "Home".
You will need to make sure that all of your machines are using the same name for the Workgroup. It can be "Home" or better yet use the name "Workgroup" for the Workgroup instead.
You should leave the Homegroup and set up a workgroup instead. Homegroup - Leave
Although it is possible to set up a Homegroup in a mixed Op system network it would be much easier to set up a Workgroup in your case. This is especially true because you only have one Windows 7 machine in your network which means that your single Windows 7 machine would not have another machine to share libraries with. For this reason there is absolutely no reason to set up a Homegroup.
As for the A/V problem, sometimes uninstalling the A/V completely is the best to fix those types of problems.