ANY question on law needs to include your general locale as laws vary by area.
If you used an inadequate extension cord for the heater and caused a fire that would have been YOUR fault not the landlord's.
It's very possible that new wiring was put in and they bypassed those outlets. So you may not have grounds for repairing the wiring yourself. As for the dishwasher, were you told it would work? A dishwasher is not a necessity and its lack of working does not make your unit uninhabitable.
The point here is that you are talking about items that do not make your unit uninhabitable, only inconvenient. And that may not be enough to take it upon yourself to repair and definitely not to withhold rent.
So my suggestion is to give the landlord one week to deal with these problems or you will report it to the local housing department. If he doesn't then you go to the housing department and report it. If they inspect the premises and issue summons to the landlord THEN you can give him a deadline to repair or you will contract for the repair and deduct it from your rent.
But don't be surprised if the housing department doesn't issue any summonses since, as I said these are not big issues.