user_* is anything initiated by the user

system_* is anything initiated by the server - statistics updates etc...

Seeks are seek operations (index seek, clustered index seek)

Scans are scan operations (index scan clustered index scan)

Lookups are only applicable to clustered indexes. They are bookmark lookups caused by when the nonclustered index not containing (seek or include) all the columns in the query (SELECT columns, JOIN predicates, WHERE predicates, ORDER BY columns). The SSMS built-in report do not report lookups.

The score in general is (seeks*10+scans+1)/(updates+1). Clustered indexes don't get penalized for updates since every table should have one, but if a nonclustered index has a higher score, you should consider changing your clustered index. Higher scores mean useful indexes, low scores mean indexes that cause more overhead than benefit. Scanning cost isn't taken into account - it is just usage vs maintenance. But a score below 0.0001 is almost for certain a useless index.

If your index_columns_include is always blank, then none 0f your indexes have include coluimns. Include columns are available for covering the query, but not for seeks - they are leaf level only. CREATE INDEX IX_table_seekcolumns_includecolumns ON dbo.table (Seek Columns) INCLUDE (Include Columns)