What are search_index & search_dataset tables for, can I clean them?
These tables are used by the site's search function, as provided by the core's Search module. They're built from your site's content, and the descriptions in code in search_schema() say:


search_dataset - "Stores items that will be searched"
search_index - "Stores the search index, associating words, items and scores"


Though you can ignore/truncate the contents of these tables to keep your database dumps smaller, they will be recreated during cron runs as your site's content is re-indexed. Beware that rebuild times can be a lengthy if your site has a lot of content.

I've always found the Backup and Migrate module to be much handier than command-line MySQL as tables and/or their contents can be ignored, plus do scheduled dumps and  have various export/import profiles.