Asking for:
a comprehensive analysis and meaningful criticism
of 35 questions is, perhaps, a little much, but I'll try to make a start with the most recent 5.
The most recent question Did Saint George actually slay the Dragon? was put on-hold for being off-topic. I was one of those who voted to close the question, and my reason was simple. This is a question about mythology, and that is explicitly off-topic, as defined in the Help Centre:
It is not about:
- Genealogy
- Asking for reference material
- Questions answered by a simple Google search or to be found in a Wikipedia page
- Predicting the future based on historical trends
- Mythology
- General (non-human) Prehistory
- Conspiracy Theories or Pseudo-science
(my emphasis)
Furthermore, the question includes an assertion (unsupported by any sources):
"Now I haven't exactly stumbled upon any dragon skeletons lately, yet, the tale of Saint George and the slain dragon is still viewed by percentages of Christian Theists to have been an actual historical and miraculous event".
And then finally, the question:
"Is there anyone within this site who believes - (or better yet, who can prove with the supplying of archaeological and skeletal evidence) that Saint George actually killed a Dragon?"
Or, to paraphrase: "Is there anyone here who believes, or can prove, this myth is true".
Which isn't a question that is on-topic for this site, as the present guidelines on the Help Centre make clear.
The question before that was Was Arabic the “Lingua Franca” of the Middle Ages?. The answer here is actually straightforward. A Lingua Franca is defined in the Oxford English Dictionary as:

Clearly, Arabic was a lingua franca in the Middle Ages, but not the lingua franca of the Middle Ages.
There is a Wikipedia page on the subject, which includes a List of lingua francas. Now, I get from your question that you aren't a big fan of Wikipedia. However, the Help Centre makes it clear that:
"Requests for trivia or basic historical facts are off-topic if they can be easily answered by looking up the relevant topic on Wikipedia. We're trying to complement common historical references, not duplicate them."
Now, I've only been using this site for about 6 months, so I wasn't involved in drawing up the rules. However, this is one that I agree with completely. (I do wish that it was applied correctly though. Too often, questions are closed for being trivial when they cannot, in fact, be easily answered with a simple Google search or by looking up the relevant topic on Wikipedia. However, that is a different question).
If you believe that the relevant entry on Wikipedia is wrong, incomplete, or misleading (which it may well be) then you need to show that in your question. Ideally, that point should be supported by sources.
All this was pointed out to you in the comments, together with the suggestion that you should edit your question so that it fit with the guidelines. You declined to do so, and the question was closed.
Your next question was What is the most historic hotel in the United States?.
The obvious question to ask here was "How do you quantify most historic"?
You haven't provided any criteria to measure against, so any answer will be based on opinion. Now that isn't necessarily a bad thing in general, and might be a great question for a debate on chat, but it is once again expressly off-topic according to the guidelines in the Help Centre:
avoid asking subjective questions where ... every answer is equally valid: “What’s your favorite ______?”
Now, not all subjective questions are considered to be off-topic. It is worth reading the guidelines for great subjective questions.
Your next question was Who coined the phrase, “The Pillars of Hercules”?. It's undoubtedly an interesting question, but - once again - it is one that is answered on Wikipedia:
"A lost passage of Pindar quoted by Strabo was the earliest traceable reference in this context."
So, as noted above, the question is off-topic here.
If you have reason to believe that Wikipedia is wrong, and that there is an earlier reference to the term than the passage by Pindar, quoted by Strabo, the you should include that information (with sources) in your question. In that case, and in my opinion, your question would have been entirely on-topic.
Next we had When does the Modern Age end and the Contemporary/Post-Modern Age begin?
In fact, you had already offered an answer to this question yourself in an answer to the question Early modern vs late modern vs post modern?. However, as others had shown with their answers to that question, there is no generally agreed consensus to the definitions, so answers would tend to be based on opinions.
Once again, people suggested that editing the question to clarify your definitions might salvage the question. Once again, you declined to do so, and once again the question was closed.
Wikipedia
I agree that one must be cautious about using Wikipedia. There have been a number of studies concerned with the reliability of the content. A few examples are:
(These particular examples are all behind paywalls, but I'm sure that a Google search will turn up other, similar, articles which will doubtless make the same points)
Personally, I am generally quite relaxed about using it to provide links to the pages for people mentioned in my answers, since this is mainly to provide background detail for people unfamiliar with the subject or person.
For example, in my answer to the question Why did the Germans spare Allied troops trapped at Dunkirk?, I've tried to link to all the Wikipedia pages for the individuals mentioned in my answer. These are not essential details, but simply background information to help those unfamiliar with the dramatis personae.
I'm also generally happy to provide links to Wikipedia for uncontentious topics, although with a note of caution that you didn't mention. While the URL to the Wikipedia page shouldn't change, the content of that page might. Almost anyone can edit Wikipedia - it is, in its own words:
... written collaboratively by largely anonymous volunteers who write without pay. Anyone with Internet access can write and make changes to Wikipedia articles
You might link to a page with content that is uncontentious, and which provides the mainstream view about a topic, a future edit may change that.
Nevertheless, for things like the British Expeditionary Force, and the background to the Dunkirk evacuation itself which I also mentioned in my answer above the Wikipedia pages again provide useful background for those less-familiar with the subject.
However, for the documents that provide the main sources for my answer (the diaries of General Halder, the note from Major-General Alfred Jodl to labour minister Robert Ley, etc.) I prefer to link to online, digitised versions of the original documents where possible.
Now, Wikipedia is getting better at providing sources for its content, but it is a slow process (see the reviews in the academic journals listed above). Wikipedia is still no substitute for proper peer-reviewed sources.
Unfortunately, many of the journals containing those sources are now only available online behind a paywall. I was challenged about this when I provided links to this type of site in some of my early answers (I pay for access to the relevant sites because I need them for research).
That seems to me to be a reasonable complaint. The point of linking to the source is to support the assertions we make in our questions and answers. If others can't read those sources, then how do they know we are quoting them correctly? How can they follow up on the answer and take their research further?
It is also clearly going to be extremely frustrating to have to search for alternatives (as you may have now experienced yourself in the case of the journal articles I cited above)!
On other questions, I have used books from my own 'library' as the source for my answer. I'm lucky in that regard. I own quite a lot of books. Unfortunately, while books are wonderful things, they can be difficult to share online. Often, those books are also available on Google Books, but Sods-Law dictates that the preview doesn't include the relevant pages.
I have often spent longer looking for decent online sources to support the points in my answer than I spent on writing the answer itself. [If anyone is interested, I've found archive.org to be a very useful resource in that regard. In particular, they have a complete series of the Congressional Record which is obviously the go-to source for a lot of American political history].
However, yes, in the final analysis, sometimes it is just easier to quote Wikipedia.
If the article there is well written (many articles are, despite the criticism you make), and if the [current] content appears to be correct, then I'm reasonable happy to include it as a link in my answer. I would argue that is generally better than providing no supporting source at all.
At least then others can review my source, and challenge it if they feel that it it wrong (hopefully they would also provide alternative sources to support their position). And surely that is, in fact, the main reason for providing supporting sources in the first place.