We don't have a knowledge base article on this yet, but we'll look into creating one. You've listed most fields that are searchable as far as I know. These are missing though:
- Description
- Domain
- User and computer OU
- Report
- SMBIOSAssetTag
For performance reasons, Lansweeper does perform a "begins with" search in many cases. You should be able to use % as a wildcard though, e.g. "%Doe". You can also "search" any database field by creating a basic report that lists all field values under Reports\Create New Report and then filtering the report results. (The search boxes in report results perform a "contains" search.)