The two questions you have asked interested Plato to the extent that he invented the inquiry of epistemology in order to answer them.
The first question: "How can one know any characteristics of a thing if one does not know what that thing is?" appears right at the start of Meno when Meno nearly accosts Socrates, demanding to know how virtue is acquired by men.
Socrates chides Meno for presuming to know what virtue itself is, claiming that he, himself, has no clear idea and so cannot answer how it is acquired. This astonishes Meno, who chides Socrates for ignorance on a matter of basic gentlemanly knowledge.
But Socrates drives his point home by asking if anyone could know whether Meno were rich or good looking without knowing who Meno, in fact, is. Meno admits that a person lacking acquaintance with him could not know such characteristics as whether he were rich or handsome.
Socrates seems to prove to Meno that knowledge of a thing is necessary for knowledge of the characteristics of that thing. So, Socrates would echo your question, "How can we make claims about knowing things when we do not know precisely what knowledge even is?"
To ameliorate that difficulty, Socrates suggests that he and Meno search together for knowledge of virtue in order to determine how it is acquired by men.
A definition of virtue is more elusive than expected and results in a separate inquiry into the distinction between true opinion and knowledge. Socrates claims that when true opinion is based on causal reasoning, it is knowledge. This seems to be the origin of the justified-true-belief definition of knowledge.
In his Theaetetus, however, Plato has Socrates explore the JTB definition in great detail, eventually rejecting it with what I consider the presentation of a Gettier case.
So, Plato seems to have had similar questions to the ones you pose here, and seems to have struggled to more than one answer to them in the case of "What is knowledge?"
Your first question: "How can we make claims about knowledge when we do not know what knowledge is?" seems to highlight our ability to intuit the nature of a thing without a fully articulated definition of it. We intuit that Gettier cases are not knowledge from some internal conviction we have of what real knowledge is. Neither Plato nor Gettier completely accounts for this.
Your second question: "What does it mean to know something?" seems to be an ongoing one. Some additional criterion seems to be required to augment JTB, or some refinement of what is meant by justification.
Karl Popper argues that knowledge is not a belief at all, but an object in the world. We do not seem, however, to have reached the end of epistemology, so apparently, Sir Karl has not definitively solved the problem, as he claims.