I have an old .45 convertible, have never used the ACP cylinder in it. Can I shoot .45 Super and. .45 AR through the ACP cylinder?

45 AR won't work, the rim is too thick.

Since the 45 super is dimensionally identical to 45 ACP, it will work fine. The Blackhawk can handle the extra pressure with ease.

If the .45 Super is the same case length as the .45 ACP then it  will fit. Don't know about the pressure of the .45 Super. I would limit any loads to 30,000.

.45 AR won't work in the .45 ACP cylinder as it comes from the factory, but it is an easy mod to trim the cylinder to allow .45 AR to properly headspace. .45 ACP will be unaffected. I have a couple of .45 NMBHs and I have had the cylinders trimmed for .45 AR. I mostly use the AR brass for range ammo because I don't like to load small charges of fast powder in the huge .45 Colt case. I reserve the .45 Colt for full performance ammo and up (slightly).

its been too long since I had mine, but I don't think there is enough relief for the AR.  As for the super, you won't hurt the gun.

Not sure how old your Blackhawk is but the new 45 Blackhawks can chamber 45 ACP or 45 AR.  Manual says so.

Mine is a bicentennial model

Call Ruger.  I am sure they would be happy to help you figure out if yours will chamber 45 Auto Rim safely or not.

.45 acp is it. However, you can load it much hotter than what is acceptable and safe for a 1911. Check out Jerry Miculeck's handloads for his S&W.