[bkiziuk]

1- When I start kodi I get a pop up at the top of the screen with some percentage of operation that the subtitle mangler is doing, how can I hide tat pop up and prevent it from appearing.

This is probably the process that removes subtitle files from disk if there is no video file accompanying it any more.
If you prefer, you can disable housekeeping in SM settings.
However, if you want it to run without any visible notifications, there's no such function built in. But you can edit the source code to remove pDialog object responsible for showing this notification:

    pDialog = xbmcgui.DialogProgressBG()
    pDialog.create('Subtitles Mangler', common.__addonlang__(32090).encode('utf-8'))
        pDialog.update(progress, message=common.__addonlang__(32090).encode('utf-8') + ': ' + source.get('label').encode('utf-8'))
    pDialog.update(85, message=common.__addonlang__(32091).encode('utf-8'))
    pDialog.close()
 

 2- the addon does not clean the subtitles from advertising. I want to provide a log so I chose to save the log in separate file because kodi log can get too big, but where is mangler saving the logs?

It should be present in the plugin's data dir.
On my PC (Linux) the location is:
/home/<username>/.kodi/userdata/addon_data/service.subsmangler/
Of course it can vary a bit depending on the platform.