OP's context is an example of OED's definition #3 for the phrasal verb to call out (first recorded 1823)...
To challenge to fight (esp. a duel).
It's effectively a figurative extension of usages such as...
"Come outside and say that!" (repeat your insult, and we will fight where it is more convenient)
...but the modern usage doesn't directly refer to fighting with duelling swords or fists. The metaphoric "weapons" which will be used in the "contest" are justifications (facts and logical arguments).
By implication, the person issuing the challenge expects to win, because he doesn't think the other person actually has valid justification for whatever he said, implied, or did. It's important to note that you can just as easily be "called out" over disapproved-of action (or inaction) as a disputed statement...
"If your husband never helps with the housework, you should call him out about it."
That's to say, to call [someone] out over/about X means to demand that they justify X.
No, it doesn't mean that (at least not in the US).
As a native speaker in the US, if I heard someone say "hit and trial" I would probably stop them and ask if they meant "hit and miss" or "trial and error".
I've never heard that phrasing until seeing this question.
In your example question from Mathematics SE, it looks like they mean "trial and error", but I get that from the context, not from understanding the phrase.
It might mean that in Indian English.
It's been suggested that this might be a phrase that's used in Indian English.
I can neither confirm nor deny this, but a google search reveals it being used to mean "trial and error" in an article written by a "Brajesh Shukla", in a question asked by a "Surya Varma", and in an article on "The Hindu". So, the suggestion seems as though it may be true.
Best Answer
The English are famously nostalgic about their naval tradition, which mostly comes from the late age of sail, 1750-1850. During that era, ships were invariably built from wood, and the sailors who crewed them are, in imagination and literature, depicted as strong and unyielding- like steel. "Wooden ships and iron men" is something of a cliche in referring to that era.
The C&H cartoon imagines an old man reminiscing about the past, and suggests that he's alluding to that era of wooden sailing ships. But his further comment in the third panel reveals that he's really talking about an (imaginary, of course) battle between a navy with wooden ships and cyborgs- men literally made of steel: robots.