OneDrive is based upon a Microsoft SharePoint backend (well, Onedrive for Business certainly is at least - we've just finished a pilot study to implement it for an entire University). I'm not entirely sure how the connection works but I believe it is WebDAV so the folder can be opened within Windows directly (in SharePoint web interface there is a button labelled "Open in Explorer" which opens the folder as if it were a normal folder).
There are "apps" available to access OneDrive files natively on some devices (obviously Windows versions have full functionality) but (at present) there is no Mac application nor, I believe, Linux either.
If you delete a file on the "local" side then the OneDrive agent will mark the file as deleted but it will move into your OneDrive "Deleted Items" folder. To recover the file, yes, you have to go to the web version of OneDrive and recover the file from this folder - a very simple process and useful to make sure your files aren't easily permanently deleted!