What does it mean for a cause to have no explanation?
It means the cause is an anchor-point for a chain of subsequent cause and effect. It's like a hook in the ceiling where you suspend a chain. The hook itself is not a link, but it provides the ability of the chain to bear weight (analogous to existence).
The principle of sufficient reason allows us to end there; but it doesn't seem clear at all to me that this sort of answer can be applied in the case of free will choices.
The laws of biology are rooted in deeper laws of chemisty, and those laws are rooted in the deeper laws of quantum electrodynamics, which are a broken symmetry of a Grand Unified Theory, which in turn precipitated out of a Theory of Everything that includes quantum gravity, and so on, until you arrive at the most fundamental and basic laws which underpin all of reality and have no further explanation, other than they were selected by an intelligent will with sufficient power to impose them uniformly across the entire universe. So we postulate that God possesses a property called "free will" which is isolated from prior causes (otherwise it's not free, by defintion). And in order to absolve God from being culpable for human sin, we postulate that this supernatural property called free will was also given to human beings (and not other animals), but it was coupled with a limited power which goes along with being finite. Thus we are able to initiate certain sequences of cause and effect for which the ultimate responsibility lies solely with us, and cannot be laid at God's door.
On the other hand, if you say that the principle of sufficient reason does not apply to free will choices, then I must ask: on what grounds?
On the grounds of the dichotomy between materialism and the supernatural. Limited to materialism, the PSR leads to an infinite regress of causes (or deeper and deeper explanations as outlined, which is a more subtle rabbit hole to follow). Thus we must postulate a supernatural (or metaphysical some would insist) intervention which rolls out from taking as an axiom that the will of a moral agent truly is free.
Moreover, does not the notion of choices as unexplained and uncaused causes put them into a position of metaphysical parity with God?
When God created man "in our image" he was not speaking of his body, because God is a spirit. He was speaking of God's mind. And God is free. So God created man free. But God only created man after his likeness, he did not reproduce himself and create little gods. Our powers are limited to what we can sense and touch, with the exception that we can communicate with God in prayer and respond to the movement of his spirit.
Going even further, does this ontological entailment not imply, a fortiori, that the originators of the choices have at least the same ontological standing as well?
Only over the consequences which roll down from our choices. Since God was there at the beginning of all things, his choices at the beginning had a universal causal efficacy.
But then, what does it mean for people to be the originators of uncaused events? How can a free will choice be mine if it is, in fact, uncaused?
There are two classes of uncaused events, random events and first cause events. When I was a child (not so long ago), we played a card game called "War" where you split a card deck in half, and each player threw down a card one at a time, and whichever card was bigger won that "trick". It was boring because it was purely random, there was no way for the player to claim ownership of their play. So how to make it more interesting? Let the players look at their cards, and look at each other. They use their judgment to decide when to play the high cards or when to sacrifice the low cards. That's the secret. Intelligent decisionmaking.