Good day,
Whilst going through the hints that have been prepared for the reviews (wonderful job, BTW), I’ve come on several occasions across the word ‘ある人’.
My question is, what would the difference be between ‘ある人’ and ‘誰か’? Is it a matter of degree of politeness (as for example ‘あの人’ and ‘あの方’) or are there other considerations to be taken into account when using one or the other?
教えてくれて置いてありがとう (if I may say so! 
)
ある人、ある会社、ある学校、ある世界、ある場所、ある日
They all mean “a certain” something. The difference is the same as saying “a certain person” and “someone” in English. They are not completely interchangeable and I doubt they have anything to do with level of politeness.
ありがとうございました。
So you could say for example ‘誰か助けて！’ but not ‘ある人助けて！’.
Further to this, would you use ‘ある人’ if you wanted to imply a certain known person? For example, would ‘ある人が僕の手帳を盗んだ’ carry the meaning that you know who that person is but don’t want to name him/her?
(I guess that it would be more proper to say '僕がある人に手帳を盗まれた, 
)
Yes, ある人助けて looks extremely off 
The go-to phrase would be 誰か助けて.
To (not) answer your second question, I know this is common in English but I have no idea whether this kind of sarcasm (is it sarcasm?) carries over to Japanese. I certainly don’t recall ever seeing or hearing this kind of usage, so I can’t help with that 
又ありがとうございました、スメレチュニさん！
Also for your non-answer, which is an answer in itself: if you haven’t come across this usage, it probably means ‘ある人’ is not used that way in Japanese.
Probably yeah, but I certainly wouldn’t bet any money on that
誰それ is used to mean “a certain someone” like the English phrase, I believe. Here is the definition from google: 何々と名前を指しては言わない言い方。だれか、ある人。なにがし。
ある人 is more like “some person” rather than “someone”, although could be translated as “someone” in certain contexts. There are maybe a couple of things that might make the meaning clearer.
1: ある日 is used in a similar way to “one day” is used in stories in English. It does mean a “certain day” but the actual day itself is not clear, just that it is some specific day at some point. The same applies to ある人 - it is “some person”, we don’t know who but we do know that it is someone specific.
2: When Japanese people learn English they use two constructions to help them understand the articles “a/an” and “the”. (This is used as a rough guide so please do not think that you can translate a/an/the into Japanese somehow - it is just to explain the basic idea.) ある〇〇 is used for “a/an” and その〇〇 is used for “the”. For example, ある一つのりんご and そのりんご。 The first means “one certain apple (which one, out of all the apples, we don’t know)” which is to say “an apple”. The second means “that apple (and we know which one)” which is to say “the apple”. If this example is confusing then ignore it as it isn’t too important but it is a context in which ある〇〇 intersects with English in Japan. I think most Japanese people understand a/an/the in these terms unless they are actually fluent in English.
Hope that helps a bit.
I’ve definitely heard things like ある and とある used in somewhat sarcastic ways, one that’s reasonably common is people avoiding using other companies or characters from other companies names, even hear youtube streamers do it jokingly at times. For example people using とある配管工 instead of Mario. As far 僕がある人に手帳を盗まれた, I wouldn’t take it as 100% but it feels to me more like it has a nuance of knowing who done it than if you used 誰か.
三人のある人に完璧な説明をありがとうございました！
If you don’t mind, I’ll note this is not how ある is used. The difference between ある人 and 誰か is that ある defines something that is not known (usually to anyone, but in some cases not known between the speaker and listener). So, for example you can’t say 真女神転生ってゲームのスクショをネットで張って、あるおっさんは懐かしいと言ったんだ because you, the speaker, interacted with the おっさん. Instead, here, you might say 知らないおっさん. You can, however, say "私の友達は真女神転生ってゲームのスクショをネットで張って、あるおっさんは懐かしいと言ったそうです " because you, the speaker, have never interacted with the おっさん and thus do not know him.
ありがとうございました。難しいね・・・