Comments - Direct Upgrade from MySql 5.1 to Maria DB 10.1
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1. The main concern with skipping versions is that, while upgrading one major version is usually well-tested, skipping versions is not, so you may bump into an incompatibility. I suggest carefully going through the changes in each release to see if any could affect you: 5.3, 5.5, 10.0, 10.1 as well as MariaDB versus MySQL - Compatibility. Many people have successfully done what you intend, but it depends entirely on your usage.
2/3. InnoDB is very different to MyISAM. It's much more robust, and there's usually no need to check and repair in the same way. See Converting Tables from MyISAM to InnoDB as well as XtraDB/InnoDB Recovery Modes for what happens when innoDB detects corruption. Usually you would need to restore from backup (drop and reload).