Google Photos:
1. No. You can only do this if you delete the picture from the Google Photos app or Google Drive
2. No. To download all the photos back to your phone, you have to do it manually. Consider it as a cloud-based storage using the Google Photos app. Also a hue caveat, if you opted for the free "unlimited" storage, your photos WILL be recompressed significantly REGARDLESS of the size.
3. No integration like that. You will have to do it from Google Photos, export and "share" to instagram
Flickr:
1. No. You can only do this from flickr's app/site. There's not even a desktop syncing client that I know of.
2. No. You are saving things to flickr server. To get photos back to your iPhone, you have to download them manually, or rely on your data connectivity to see your photos from the flickr app.
In the end, any other services can only provide a half-way service. Nothing will truly integrate with Photos app on the Mac.
3. Same with above, you have to pick the photo from flickr first, then "share" to instagram.
Unfortunately there will be no truly integrated 3rd party service on iOS to match iCloud.