This question collects together a number of different, but related issues, so detailed responses to the specific cases are appropriate:-
Take your second paragraph -
But what about terms that seem to contradict each other given their implied meanings? For example, what about a “five armed human”?
This is a version of the "black swan" case. In such cases, there is always a choice to be made, whether to include the new case within the definition or not. So when black swans or five-armed humans are discovered, the concept can be expanded (as happened in the black swan case), or the new case can be defined as a new concept. The choice does not need to be arbitrary - the decision to include black swans as swans, for me, is perfectly rational. This just shows that definitions do not necessarily cater for all possible variations in advance and decisions sometimes need to be made.
Your third paragraph asks
... how does one differentiate between the logically impossible and meaningless? Isn’t part of what makes something meaningless also what we know to not be possible, such as a five armed human? And yet, clearly “Jr heheh rurjrbr rhrur” seems much “more” meaningless than a five armed human.
The difference between the logically impossible and the meaningless is often not well-defined in much philosophical discussion. For me, the difference is that something logically impossible can serve as the premiss in a reductio ad absurdum argument, which is undoubtedly meaningful. But letter (or, indeed, word) salads like "Jr heheh rurjrbr rhrur" cannot. There are varieties of nonsense. "'Twas brillig and the slithy toves/ did gyre and gimble in the wabe" is another one. See Jabberwocky
Your fourth paragraph asks
... many argue that some of His attributes (such as omni-knowledge and human free will) contradict each other. People have often tried to get away from this contradiction by saying that God attains knowledge from “outside time”. Is this a rightful evasion or meaningless?
On the face of it, "outside time" must be a metaphor, since time is not a spatial concept and consequently has no "outside". But the phrase seems to have some sort of meaning in mathematics. In addition, the "timeless present" is a firmly established concept - see, for example, Timeless present examples. Formal logic often relies on this use. One would have to find out what is meant by "outside time" before proceeding to argue about it. It may well be that the discussion will get bogged down in the preliminaries, but that itself would be a victory of sorts.
Your fifth paragraph is
Similarly, some physicalists have argued that a purely immaterial cause (I.e. a mind without a body for example) causing physical effects on the world is impossible. If it is, in what sense? Is it metaphysically possible, logically possible but metaphysically impossible, impossible in both senses, meaningless, or what?
This is the classic objection to dualism and seems conclusive to me. But clearly not everyone agrees, and the concept of a "field" in physics is an awkward case. However, if something can cause a physical effect, it is a physical something. So a field counts as physical, but not as material.
Finally, you ask:-
Can one “redefine” terms or propose ways of rescuing these potential contradictions with the phrase “unmarried bachelor” as well?
It isn't clear what you have in mind here, but if the use of a word can change over time, one couldn't rule out changes in the use of "bachelor" that would change the status of "unmarried bachelor".