Is there any chance of data loss?

No. The add-on creates a *new* database. Once the operation completes, it'll clean up older databases, but only databases that have been created by the Migrate add-on.

Is there any chance of data skewing?

Yes. If the remote database is in use, it's possible that the data changes during a 'pull'-action. E.g. a user may be adding blocks to a page, or a form may be submitted. In order to maximize data integrity, consider putting the remote website in 'Maintenance Mode'. Also, inspect whether Automated Jobs are scheduled and or running.

Where do I install this addon?

On the website you want to pull to and the website you want to pull from. Don't worry about the licensing, once you buy this add-on, you may use it on all your websites.

Why doesn't it support pushing a database?

Because I can't guarantee the working if the remote database is being used. I also don't want to risk any chance of data loss. And a final reason is that creating a database on a production server, is probably not allowed most of the times. I'd recommend you to use a database manager or a tool like mysqldump if you want to push a database.

Why does it change my database name?

Because the add-on creates a new database. It uses the profile handle and a date time value to make the database name unique, each time the pull command is issued.

My table casing is incorrect

If you're a Windows user, you might want to look into the MySQL global variables. It's not related to this add-on though, but there are plenty of threads in the forums about this.

MySQL aborts the connection

If you get this error: "Got an error reading communication packets", try to optimize MySQL, or restart the service to free memory.