Once an item sells, do we remove it manually from the inventory?

Short answer is no...

The longer answer is that when you record the sale, if you select the inventory item, it will be transferred from inventory into sales when you record the sale. To select the inventory item:

1. If you are recording the sale manually, in the "Item Sold" box, search for the item in inventory and click on the item that you want to mark as sold. Once you've clicked it, don't modify the title because this will deselect the item and create a new item for your sale.
2. If you are recording sales via the daily eBay integration (Ultimate Only), read here: How the daily eBay integration works
3. If you are recording sales via the bulk sales matcher (Ultimate Only), read here: How to bulk match sales to inventory