I use MySQL as my database engine. How can I see how the database engine resolves queries internally?
It'd help if we know what you wanted to use the tool for.
From my experience, even if such a thing were available for MySQL, it's not something I'd use for analysing/tuning performance. For general database setup I've found mysqltuner.pl does a very good job. While for schema / query tuning, I use mysql_slow_log_parser along with some crude scripts to prioritize problem areas.
For monitoring availability, I use Nagios - which also monitors all sorts of other services.
Some discussion of the same topic on Stackoverflow
There's several websites and books on the subject - mysqlperfromanceblog is a good one
If all you want to see is how sql queries are resolved internally, use EXPLAIN (aka DESCRIBE)