1) Instead of categories, the Auctiva store allows you to create custom searches to allow users to search your inventory. To set up a custom search, please fo to Auctiva -> Store(Tab) -> Customize your Store -> Select/Edit, and click the "Custom Searches" link.
To add a search to your Auctiva store page, just select the link text, keywords, and search logic for your custom search and click the "Add" button.
Then, when a customer clicks on this search on the left hand column of your Auctiva store page, a list of items whose titles contain the selected keywords will be displayed. The results will either display the items that contain all or any of the selected keywords will be displayed depending on the match logic you have chosen.
2) No, unfortunately, the Auctiva store window cannot be set to display items in a particular category based on what listing is being viewed.
The store window is set to display 14 of your active listings at a time and is refreshed every 2 hours. Each time the store window refreshes, it is populated with another 14 of your current listings that are ending around the same time as the next auction of yours that is viewed.
The only way you can control what goes in your store window is by making items hidden. To do this, go to Auctiva -> Store(tab) -> Edit Items. Items that are made hidden will not be shown in your store window the next time it refreshes, which it does about every 2 hours.
3) No, it is not possible to disable the link/search feature on the Auctiva store window.