To what extent can we monitor jobs/suspended queries as DBO
Though logging into the machine and analyzing the wait chain on the Resource Monitor could give some extra info (for instance if sqlservr.exe thread is blocked waiting for lsass.exe it could mean it is blocked at a authentication validation), what you'd really want is to be granted the VIEW SERVER STATE permission so you can view the DMVs that might help you, like this ones, for instance:

SELECT sqltext.TEXT,
 req.session_id,
 req.status,
 req.command,
 req.cpu_time,
 req.total_elapsed_time
 FROM sys.dm_exec_requests req
 CROSS APPLY sys.dm_exec_sql_text(sql_handle) AS sqltext 
order by cpu_time desc