In short: Yes and yes.
Slightly longer version:
call GET layouts with embed parameter set to regions,playlists,widgets
can be used to get the playlistId and widgetId
Once you know that you can:
Remove widgets - Swagger UI
Regarding playlist/order/{playlistId}
Let’s explain that on an example.
I’ve created a new layout id 79, added 2 images to a single region.
So I will call
/api/layout?layoutId=79&layout=&embed=regions,playlists,widgets
Which will give me my playlistId (151) and widgets Ids (270 and 271)
now I can call the /playlist/order/{playlistId}
ie in my case
/api/playlist/order/151
that call takes an array of widget Ids in a parameter called widgets with values corresponding to the display order in which they should appear.
ie if I would want to reverse the order of my images I could do it like that:
so now widgetId 270 will have displayOrder = 2 and widgetId 271 will have displayOrder = 1
I hope that helps, if anything isn’t clear please ask.