Unless your tracing all your queries you wont know about deletes, for drops if your quick enough you could look inside the default trace, but that gets overwritten quite quickly so you would need a process to load in the trace files before they get overwritten.

Easiest option is to put a DDL trigger on the databases in question for the DROPs and then put DML triggers on the tables you want to know who's deleting from to farm out the username and a timestamp when a record is deleted. But this will be a going forward audit, not a back in time audit.