Empty gray cells in the results table are shown when multiple editions of a release are listed consecutively, to avoid repeating shared information. Just look up to the next non-empty row. If something is empty and it's not gray, that means the information just isn't in the database.

Album Name checks against Japanese, transliterated, or translated names. % is the wildcard, so a search for %love% will find albums that used love or words that translated to love.

Credits: Probably quicker to show a few examples than try to explain it in full. != is the way to express "not".
[Artist=Minimoni]
[Artist=%Musume%] and [Artist!=Coconuts Musume]
[Producer!=Tsunku]

Release Date: Use YYYY-MM-DD date format.

Edition: Can specify particular edition like R or LA, or again use wildcards. % for multiple characters, _ for single characters.

Catalog Number: Same as dealing with the earlier text fields.

Order By: Usually just clicking on the column headers will be fine, but you can also combine them here, like
AlbumType ASC, Seniority ASC
Artist ASC, AlbumType DESC