To include an indirect object in the first two, you need a bitransitive verb. In the second one, iuvare is a bitransitive verb, so just add in the "me" somewhere.
Quis potest me iuvare aperire hoc?
A more Latin (SOV) word order would probably be:
Quis me iuvare hoc aperire potest?
Also, the "hoc" needs to agree with the gender of whatever you are opening, whether you actually state it or not. If it's not neuter, than it would have to be hunc or hanc instead. If it were a box, it would have to be hanc, because it would be short for "hanc arcam".
I don't actually know what discernere translates to, but I think I can guess.
If you were just "telling" what something was, as in the English cognate discerning, than that would be fine - but discernere isn't a bitransitive verb in the same way that in English you can't discern something to someone. There are only about a billion uses for "tell" in English, and I think the one you need is narrare.
Quis potest mihi narrare...
It's mihi instead of me above, because iuvare is a weird verb that takes two accusatives, as opposed to narrare, which takes an accusative direct object and a dative indirect object (mihi). That's standard. There are a few like iuvare that don't though.
The rest of it is harder because it's indirect discourse. (Also, I think "arcanus" is secret.) I don't want to get into it (unless you want me too...
), but I think it would be:
quem arcanum adsit.
Altogether this is:
Quis potest mihi narrare quem arcanum adsit?
or
Quis quem arcanum adsit mihi narrare potest?
Edit: Also, "quid" declines like the relative pronoun, and has to agree with arcanum.
Ipse isn't "very" - it's a reflexive something or other to refer back to the subject. If you want to use "very" with an adjective, you have to use the superlative form of it. So "very puzzling" would translated into "most puzzling" in Latin. Most puzzling.
And "perplexus" has to agree with the box in gender.
Arca perplexissima est.
The last one isn't bad, but you should translate "key to mystery" as "key of mystery" with the genitive. And remember to make the adjectives agree.
Instrumenta aenea tenent clavem arcani.
or
Instrumenta aenea clavem arcani tenent.
Hope that helps.
Edit: Messed up the indirect discourse after all. Fixed now. *curses evil subjunctives*