1) They are very stable, as stable or more so than the Microsoft counter-parts.
2) You can create your own backup scripts and cron them to ensure they run automatically. The scope of your backups can range from database structure to actual database record values.
3) You will need to install the ODBC drivers on your clients, and reference them accordingly. These are available from mysql.org
Note:
MySQL and SQL 7's date formats are different. Additionally, MySQL does not support the INNER JOIN, LEFT JOIN, and RIGHT JOIN statements, so you may need to create some recordset recursion. There are other language differences such as GetDate() versus Now(), SubString(), the "Select TOP" versus "Limit", etc.
These changes may require recoding of the applications you use. It is recommended that you research the language differences in these products before you start to implement such a drastic change.
Hope this helped,
Nathan