A Mig-27 is the ground attack version of the Mig-23
Correct, and similar to the SU-24 in appearance.
Yes, but to complicate matters somewhat, the export versions, aka monkey model, of the -27 are nomenclatured -23. Biggest visible difference is the radome. Large and fat on the -23, smaller and pointier on the -27. Some differences in the engine inlets and undercarriage too, IIRC. Those are old birds, not quite as old as an F-4, but technologically similar to early F-4s.