Nop it has not been tested with Shortpixel.
I assume that Shortpixel only replaces the actual image content by an optimized one. Then you should not have problem with the main content, I mean the post content.
I don’t know how the plugin deals with keeping an history of what has been optimized or not, you could have some issues here but nothing that could break your website.
You should not have any problem with woocommerce but always make a backup of your whole site before using the plugin.
What it does is not a common practice and WordPress has not been built to allow that.
No the plugin replace all urls it finds in all the database tables.
It has to because if an attachments is actually moved, all references to this file would be broken, if it’s not replaced in all tables it.
Best regards