Mobile sync to Lightroom Classic cleanup

I use Lightroom mobile on Ipad and Iphone when travelling and understand how that works. What is confusing to me is that I have set up all of my iphone photos to be synced to Lightroom Classic also on my MacBookPro. They are not in a collection, they are in a folder just like any other folder imported to Lightroom. 

I want to stop this and then move forward to only syncing what I want through Lightroom Mobile, however, I don't know whether once I delete from the cloud whether downloaded files will remain on my computer?

1. I did move some vacation photos from the Lightroom mobile download file to a vacation folder and still see the synced symbol. Does this symbol stay even if I delete the photo from the cloud storage? 

I want to keep these downloaded files on my computer. 

2. When I delete synced photos from within Lightroom Classic - are they deleted from the cloud? Or would it be better to delete from the cloud?

The directions for how synced photos are stored should have a flowchart. Thank you.