The 5th, 8th and 13th Amendments and their various interpretations in court opinions: this is a good place to start learning about prisoner rights.
Some argue that prisoners do not enjoy access to any constitutional rights, or perhaps only a few of them. But if this were true, surely the Constitution would have explicitly established them as a specific underclass, as it did for slaves.
The constitution does actually explicitly establish convicts as a specific underclass; in fact it literally specifically allows them and only them to be slaves. The 13th amendment reads:
> Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
The 13th Amendment belongs to a different document than the Constitution proper and was ratified about eighty years later. From the standpoint of the dominant school of constitutional interpretation, the distinction matters.
You're going to have to clarify what you mean on that. I'm not aware of any school of thought that thinks amendments to the constitution are somehow distinct or less valid. The original document provided processes for amending (i.e. modifying) it, and amendments were made under those rules. An "amendment" is literally a modification to a document; that's what the word means.
In fact, to the extent that there's a distinction, it's that amendments take priority over the previous version of the document. Obviously they'd have to; otherwise that would just mean you can't amend the original document.
According to the current version of the US constitution, which is the only one that matters, slavery is legal in exactly that one circumstance.
Some argue that prisoners do not enjoy access to any constitutional rights, or perhaps only a few of them. But if this were true, surely the Constitution would have explicitly established them as a specific underclass, as it did for slaves.