Re-surfacing the disc is very much depending on the condition

The disc for this car could be a bit too thin for re-surfacing judging from the age. Also it depends on how deep the groves are. But just in case it’s still thick (e.g. replaced before) and not too bad in term of roughness, it’s not necessary to replace. Re-surfacing is just fine since I’ve done that before. Because this is safety related and I'm pretty sure that garage will insist on replacement if it’s so out of shape.

One thing is for sure in this case, the brake pads need replacement ASAP since it’s making so much noise. It’s quite a common mistake for many people (including myself many years ago) who are not so familiar with brakes and insensitive to the early symptoms, or maybe simply too lazy. If this is not taken care of for too long, the metal bolt(aslo a safety measure so we know the pads need replacement) inside the brake pads will create deep grooves in the disc, and it’d be too late to do re-surfacing.