As far as the plastic center emblems on the full wheel covers, you can bend back the tabs on the back to take them out, but the tabs will most likely break off. Then the only way to get the plastic centers back in is to glue them in carefully by squirting roofing sealant around the edge and inserting them back in the hole.
The old plastic centers can be fixed up good enough for a daily driver by polishing out the backside and painting them red but they wont look like the original finish. Or, you can buy new plastic center emblems from many of the resto parts suppliers and glue those in.
I have used Grundy Plastic cement before and it still holds up to this day. Black-Jack roofing cement might be similar, but can't guarantee hold.
Use coarse rubbing compound at first on the plastic centers then go to a fine compound and slightly moist cloth.
If the plastic centers are displaying excess crystal checking, they wont look good no matter how much elbow grease you put in to them. Just buy new ones. They ain't cheap though.