I believe the reason for the troubles on this game, or at least these two questions, may be the set up.
I will be thorough in my explanation and the thought process I had when I sat down to do this game.
After reading the logic game prompt without reading the indented rules, I had this as my set up.
I chose the illnesses (5 of them) as the base of my set up. This is because I know that each of them contains at least 1 symptom. There are 3 symptoms available to us. However, at this point, there is nothing telling me that I must use all 3 or even two of them. Too much uncertainty using the symptoms as the base. I know the illnesses must be used, as each has at least 1 symptom.
As of now, I simply place a slot next to each illness because I know they have at least one symptom of F H S.
Next, I go through the rules.
After reading rule 1, my diagram looks like this:
I know that J has H and S as symptoms. However, it does not say that it
only has those symptoms, or is limited to those. For now, I cannot preclude the possibility of F also being a symptom for J. I keep that in mind.
After reading rule 2, my diagram looks like this:
This rule told me that J and K have none in common. Since each illness has to have at least one symptom, and J has 2 of the symptoms, then K must have F. We also know that we can "wall-off" both J and K. We know exactly what they have. No chance that K could have 2 or 3 symptoms and no chance that J can have all 3 symptoms either.
After reading rule 3, my diagram looks like this:
J and L have
at least one symptom in common. I know that J has H and S, so L must have at least one of H and S. It could have both H and S. It could have all 3 as of now. I do not wall anything off.
After reading rule 4, my diagram looks like this:
For L to have more symptoms than K, L must have at least 2 symptoms since K has one and only one symptom. I do not know what will encompass this second slot. I still could have 3 symptoms. This second slot could be the second of the H S combo, or it could contain an F while the first slot takes care of the "at least one of H S" concept we discussed earlier.
After reading rule 5, my diagram looks like this:
For L and N to have no symptoms in common, L must have only 2 symptoms and N can only have 1 symptom. We knew going into reading this rule that L had to have at least 2, but we now know that having all 3 symptoms is out of the question because L and N cannot share any symptom.
After reading rule 6, my diagram looks like this:
For M to have more symptoms than J, M must have all 3 symptoms because we know that J is walled off at 2 symptoms.
M has F H S.
Notice that after reading all of the rules and looking at our diagram, only 2 illnesses have uncertainty with them, and it is not a great amount of uncertainty. We know that L and N cannot share any. And each is walled off, so we know how many symptoms each contains.
I decided to show the only two possible scenarios for those 2 illnesses because experience tells me that this will put time in the bank to answer the questions. I mean think about it, these are the only 2 uncertain aspects in the game, you know the questions are going to address this.
My two scenarios of L and N:
When N has F, we know that L has H and S.
The only other scenario that exists is for L to have F and one of H and S, while N has the other variable of H and S.
Now, tell me if those questions do not look easier.