Where does Dashboard Cleaner store its data?

Its settings are saved to the database, but the filters are saved to a file named dhcl_xxxxx.filter and located inside the /wp-content/uploads/dashboard-cleaner/ folder (single installation) or the /wp-content/uploads/sites/X/dashboard-cleaner/ folders (multisite installation). Removing or renaming that file will simply delete your filters without affecting Dashboad Cleaner settings.

What is the difference between hiding an element and making it invisible?

Hiding will remove the element and the space it occupies; making it invisible will mask the element but will keep the space it occupies. Hiding the element is the preferrered method but in a few cases, it can wrongly alter the whole page layout.

Shall the filter be based on the exact attribute value, or can it be shortened (i.e., partial match)?

Partial match is accepted but whatever value you enter, it must start and end on a word boundary (as opposed to a substring). For more details about this, see the contextual Help tab in Dashboard Cleaner Settings page.

Are field values case sensitive?

The attribute value is case-sensitive, the HTML element and attribute names aren’t.

Will it slow down my site?