How can i disable Ordering tags, under layout options, inside the Mosaic module?

Whenever I delete these tags, hit 'save & close' and then reopen the module to make additional changes these tags are replaced by default.

I would like to be able to 'save & close' and then reopen the module without having these tags automatically set.

Thanks.

problem not solved

You can not delete them all. Delete everything, except "default".

If you want to hide everyting you have to add some code into the css/custom.css

.sprocket-mosaic-order {display:none}

Is it possible to display the tags underneath the content rather than above?

Sure everything is possible.
But then you have to create an override for the roksprocket module and edit the php file.