Header above item list displays number of results returned, as well as sort by field and sort direction
By default, results are always sorted by name ascending and always have the option to sort by name. To change sort direction, simply click on asc, toggling it to desc (descending order).

Additional sort fields become available, if you add properties to 'Must have' in Affects field. Each property added, gives option to sort by.
In addition, item list shows the value for the property added to Affects field. (suggested by Quint)
Normally, item list would show the property it is sorted by, unless you sort by name, in which case the first added property in 'Must have' is shown.

To show/hide advanced item search, click button entitled 'Advanced item search' on top right side of the window.

Advanced search comes in two flavors: basic and complex. You can toggle complexity by clicking on 'toggle complexity' in advanced search title.

Form employs generic fields, like text inputs and dropdowns, as well as a custom controls to set 'have/not have' on various fields.
This control is easy and intuitive to use, but short description is given below nonetheless.
Control enables setting of properties for various fields: must have are properties that field must have and must not have those, that item must not have.

When more than one property is added to either side, AND operation is applied. That means, for example, if slots has TAKE and BODY properties set, search will return matches that match items where slots is both TAKE and BODY. It will not match those that have TAKE or BODY!
Negative side operates in the same fashion it only negates the operation.

You add properties to either side by clicking on the appropriate (click to add) option.
Once clicked, selector is shown with all the properties for that field listed.
You can use mouse to click on properties to add them, or use UP/DOWN arrow keys to select property and pressing enter key to add them.
To remove added properties, simply click on them. Optionally, you can click on [clear all] to remove all properties for specific field.

Some selectors will show many properties, so scrolling down to appropriate one might be time consuming. For this reason, you can filter shown properties by simply typing in the letter for filter.
Typed filter is displayed on top of selector. Pressing backspace will clear one letter; pressing ESC will clear the filter all together.
Please note, you do NOT need to click on filter to 'activate it', simply start typing desired letters.

When filter is applied, filter background color changes to greenish. If filter displays no matches, background color turns reddish.
With no filter applied, color is default gray.
You will notice that filter will not trigger on single letter, it takes at least two letters for filter to be applied.

Once done, simply click submit button and results are displayed. If you wish to quickly clear the entire form, clicking on 'Clear form' button will accomplish that for you.