When I checked your six examples a couple of hours ago, they had the following vital statistics:
1. Posted 10/24/2017, 45 views, 2 upvotes/1 downvote, 0 answers
2. Posted 3/27/2017, 592 views, 1 upvote/0 downvote, 2 answers (3 up/0 down: 2/0 & 1/0)
3. Posted 12/30/2016, 6,473 views, 0 upvote/0 downvote, 0 answers
1. Posted 7/24/2013, 6,787 views, 25 upvotes/1 downvote, 12 nondeleted answers (142 up/3 down: 56/1, 20/0, 19/0, 12/0, 11/0, 10/0, 8/2, 6/0, 4/0, 3/0, 2/0 & 2/0)
2. Posted 5/24/2014, 2,726 views, 8 upvotes/0 downvote, 9 nondeleted answers (15 up/2 down: 2/1, 7/0, 4/0, 1/0, 1/0, 0/0, 0/0, 0/0 & 0/1)
3. Posted 4/16/2017, 154 views, 7 upvotes/0 downvote, 6 nondeleted answers (12 up/1 down: 5/1, 2/0, 2/0, 2/0, 1/0 & 0/0)
The two closest matches in terms of page views are #3 from group 1 and #1 from group 2. The level of total viewer interest in these two questions appears to be quite close: #3 in group 1 (posted 10 months ago) is only 314 page views behind #1 in group 2 (posted more than four years ago).
But the numbers for question upvoting, question answering, and answer upvoting are strikingly different. The group 1, #3 question has received 0 upvotes and has drawn 0 answers, while the group 2, #1 question has received a net 24 upvotes and has drawn 12 nondeleted answers that have received a total of 142 upvotes and 3 downvotes.
How can we explain this tremendous difference in voting and answering with regard to two questions that have received, respectively, 6,473 and 6,787 page views?
It can't be that site visitors aren't interested in the group 1, #3 question. At the rate its page views are accumulating, it will surpass the total page views for group 2, #1 by the end of the year. And yet no one has attempted to answer group 1, #3 and no one has upvoted or downvoted it.
A deep dive into group 1, #3
One theory might be that people who have looked at group 1, #3 have been irrationally unwilling to upvote it even though it is a "good" or "good enough" question. Another possibility is that it is a very difficult question to resolve, which discourages people from answering it or upvoting it. A third possibility is that it is flawed in some way that makes it unappealing to people who might otherwise be able to put together a reasonable answer to it.
I suspect that the third theory—or perhaps an amalgam of the third theory and the second theory—is the likeliest to be true. The header asks when one should use "relate to" and when one should use "relate with." The body of the question proposes a hypothesis that "relate with" applies to people and "relate to" applies to things, and then asks for a rule about using one phrase or the other.
According to the hypothesis in the question, people tend to say things like "how do you relate to President Trump's immigration policies?" but "how do you relate with President Trump?" Some people may divide their usage of "relate to" and "relate with" in that way, but in my experience most people do not. Further, I suspect that there is no rule one way or the other governing the use of "relate to" and "relate with."
Here is an Ngram of the phrase "relate to him" (blue line) versus "relate with him" (red line) versus "relate to it" (green line) versus "relate with it" (yellow line) for the period 1900–2008:
As you can see, the incidences of "relate with him" and "relate with it" very nearly flat-line, while the incidences of "relate to him" and "relate to it" are quite healthy—and track each other fairly closely until about 1980.
Also, if you look at the linked matches beneath the chart in the Ngram graph version of the chart, you'll find lots of examples in recent years of sentences like "None of the Zambians had any reason to relate to him" (1984) and relatively few sentences like "The more he could get people to relate with him, the more these people would lean in his direction without even knowing it" (1998). You'll even find some sentences like "They actually relate with it through the set of elements that they have placed between it and themselves" (1998). Clearly if there is a rule about using "relate to" with objects and "relate with" with people, a lot of writers aren't following it.
But there is another complication: "relate to him" and "relate to it" don't just mean "feel a connection to [someone or something]"; they can also mean "tell [someone or something] a story or narrative." Consequently, the Ngram chart is unreliable as a gauge of "relate to" versus "relate with" in the narrow sense of "feel a connection to [someone or something]."
So we're left with anecdotal evidence that writers don't widely follow a rule that "relate to" goes with things and "relate with" goes with people, suggesting that for practical purposes there may not be any such rule, plus an Ngram chart that, though impressive looking, is essentially useless owing to a confounding variable. To my mind, that's a poor basis for a convincing answer—especially if the preliminary data puts the answerer in the position of trying to prove a negative in answer to the posted question. I wouldn't be inclined to submit an answer to group 1, #3 on that basis, anyway.
A shallow dip into group 2, #1
Group 2, #3 asks for an idiom that describes "a magic object or idea that fixes everything." It's a simple question with many possible answers. The obvious single-word answer is panacea, which happens to be the highest-voted (and accepted) answer. But there are lots of other possibilities.
People love answering questions like this one, and they love to check the answers that others have suggested, and they tend to upvote ones that either match what they would have suggested or strike them as good ideas they hadn't thought of. Back in 2013, I often added my two cents to questions like that one, which is why one of the answers is mine (I also upvoted the question). But there is no mistaking the answers or the question for anything profound or carefully researched. The whole page is essentially fluff.
But people like fluff—and they especially like fluff involving single-word and phrase requests. They just do. The idea that questions like group 1, #1, #2, and #3 could become as popular as questions like group 2, #1, #2, and #3 if only people would upvote them more freely is based (in my opinion) on a misunderstanding of the huge difference in voting power and voting behavior between "word and phrase request" voters and "grammar, usage, and etymology" voters. The two groups do overlap to some extent, but in general they aren't engaged in the same activity, and they are looking for very different sorts of entertainment at this site.
I think that people at English Language & Usage upvote questions that they find interesting and that meet or exceed their criteria for baseline acceptability as EL&U questions. I don't think that people would post better questions if those questions received a stronger positive response in the form of upvotes. It certainly doesn't seem to be happening with SWRs/PRs/IRs—and many of them get lots of upvotes.
If you have a question that you think is interesting, and if you can meet the threshold criteria to avoid having it closed, I don't see why you wouldn't post it. A question that is "good enough" rarely becomes a target of heavy downvoting—and if no one upvotes it, so what? It's there because you care about it—and maybe an answerer will care about it, too, and try to offer a useful answer to it.
That, I think, is the most that any question asker can reasonably hope for from this website.