There is a thing called "government". Certain prepositions use certain grammatical case, no matter what meaning it conveys (or several cases for different meanings). For example, "с" mostly uses either Genitive ("away from", for objects you would use "на" to say "to") or Instrumental ("with"). Rarely Accusative (to talk about an approximate size: "с тебя ростом" ~ "around your height"). So when you use "с" for any "A with B" meaning, you can be pretty sure it uses Instrumental.
However, the rules of use differ between languages even when there is a rough correspondence between prepositions (eg. "на"="on", "с"="with", "to"="к", "for"="для/за" and so on). In Russian "with" is expressed just by Instrumental alone (no need for prepositions) when you mean "by means..." But when what you mean is "someone accompanied by something/someone" or "something with something added" - then use "с" + Inst.

So, I believe, it is not exactly a problem, whether you should use Instrumental or not. It is a more complex one: is a certain construction appropriate for a certain meaning or not, and when it is, the cases are mostly predictable (unless there happens to be a set expression for your specific phrase, which may have an arhaic case usage - i.e. not intuitive).
Technically, for 1), 2) 3) your suggested construction ("c" + Inst.) works:
1)Ученик с дислексией.
2)Я помогаю изучающим английский (разобраться) с синтаксисом (or, as others suggested, "помогаю с английской грамматикой", which is somewhat broader area than just syntax)
3) Джесс помогал ему с плаванием.
However, for 3) there are better ways to say it, like, the use of infinitive and then further rephrasing (помогал научиться плавать/ учил плавать/ занимался с ним плаванием and so on).