I'm writing an essay and I want to write:
These things all prove that Hitler was not a man of his word …
So should England have trusted him?
and then continue with my next points.
Is this OK, or too informal?
Ellipses have only one place in most formal writing: inside a direct quote. Then they have two uses: to reporting halting speech, and if you omit some words. But in the latter case they should be used only in non-controversial cases, as they can easily be used to subvert the original author/speaker's meaning (for example "these are... the droids you are looking for"). I suggest this means that they should be used sparingly, but use dwell they can aid clarity by omitting irrelevant material.
If the original contains a list of members of a class, and you want to cite that source to say that certain entities are members of that class, you may not want the entire list, but may need the first and last items. A toy example: "according to Smith the letters of the alphabet are 'a, b,... y, z'". This is similar to the mathematical use in a sequence, but of course in general lists aren't ordered, and not everything that can be elided is a list.
In your specific example, a comma would serve the meaning just as well. A harsh marker (if this is assessed work) or reader could interpret ellipses in the middle of a train of argument as "I can't be bothered with this step". Even when it's a trivial step you don't want to give that impression
In a formal essay, you should not use ellipses. Ellipses are a form that is mostly used in fiction, as it implies a dramatic pause, would could both upset the serious tone of the essay and imply feelings towards the reader, which a formal essay is not intended to do. If you feel as if the ellipse is intended to provoke a feeling from the reader you should not add it. An essay should have the reader gather facts and have their own feeling of their interpretation of said facts. There are exceptions, such as using ellipses to partially quote a source. This is to say that I do not recommend you using ellipses when creating parts that are not direct sources and could be used to attempt to provoke emotion from the reader.
Generally I would have said no, but I’ve noticed that the extensive use of ellipses was a distinctive feature of middlebrow historian Bruce Catton’s work. See, for example, page 26 of this best-seller of the 1950s, where he begins a paragraph(!) with them. So maybe I would say, use them, if you have a distinctive narrative style.
Yes, to all of the above - in math and lists and proper direct quotation, etc., but thank you @Delta Escher: you clearly describe the "why" of not adding it. (I recently almost lost my marbles trying to study for an English test that included formal essays - the tutors I worked with all said ixnay on the "evocative" stuff.) To impart feelings to the reader or try to elicit feelings from the reader influences/undermines the writer/reader relationship! I so did not get that til just now. (I'm into poetry.)
Here's where this realization has led me to regarding OP's example: Maybe the informality issue lies more in the question "?" format than the "..." Or in the combination of the two.
For me, the ellipsis is telling me that you as writer want me as reader to know that you are wanting me to mull for a moment, or to think that you're still mulling over all that "proof" you just laid on me...then the next thing you do is ask me a question that I know that you know I can't respond to...So maybe you're trying to have an informal dialogue with me about Hitler's lies and England's trust? Or you want me to read the conversation you're having with yourself about it?
I would say for both content and context, keep it formal. Ixnay on the style-usage of ellipsis and question formatting, and adhere to the rule strictly.
(If you want to reflect any questions that were posed regarding that topic, at that time in history, by or to England itself, you can do so without asking it yourself or posing it to your readers.)