Most efficient way to get stats on an entire SQL Server database
For checking fragmentation in 2005/2008 you can use the following script.  You need to set the @DB and @Table values.  If you define those as NULL then it will run on all databases and/or all tables.  If you do a single db make sure you execute in that DB's context (USE MyDB).

SELECT 
    object_name(IPS.object_id) AS [Table Name], 
    SI.name AS [Index Name], 
        CASE IPS.Index_type_desc
            WHEN 'CLUSTERED INDEX' THEN 'Clustered'
            ELSE 'Non-Clustered'
        END AS 'Index Type', 
    IPS.avg_fragmentation_in_percent as 'Avg Fragmentation (%)', 
    IPS.avg_fragment_size_in_pages as 'Avg Frag Size (pages)',
    IPS.page_count as 'Page Count', 
    IPS.forwarded_record_count as 'Forwarded Records',
    --IPS.avg_page_space_used_in_percent as 'Avg Page Space Used (%)', 
    --IPS.record_count as 'Record Count', 
    --IPS.ghost_record_count as 'Ghost Record Count',
    IPS.fragment_count as 'Fragment Count'
FROM sys.dm_db_index_physical_stats
    (
        db_id(@DB), 
        OBJECT_ID(@Table), 
        NULL,
        NULL , 
        'LIMITED'
    ) as IPS
JOIN sys.indexes as SI WITH (nolock) 
    ON IPS.object_id = SI.object_id 
    AND IPS.index_id = SI.index_id
ORDER BY 1,3,5


For autoshrink you can just check master.sys.databases:

select * from master.sys.databases
where is_auto_shrink_on = 1