Can I run only a subset of the inventory in a certain round?

The Asset Review round, designed to exclude from division those items that nobody wants, includes the entire inventory, so it's not possible to focus a subset of the inventory in this first round. (Although it will not include assets set to "Sell or donate" -- the very purpose of an AR round is to compute which assets are going to "Sell or donate".)

But when creating the other rounds, the administrator can choose which assets to include. So yes, in the Emotional Value and Selection Order rounds, you can specialize in a category or room or any other criteria.

As an administrator, when you are creating the round, there is a step called Select assets to be included in this round. Therein you can filter the inventory by category or room. What you need to do in that page is select items by clicking on the leftmost column (the one with check marks). You can select (or unselect) all the currently visible assets by clicking on the header for that column. Using these tools, you can select all furniture or all art with 3 mouse clicks.