Whilst you can use all three in both sentances there is a major diference between hardly and rarely/seldom that makes the second sentances context dependant.
2 (a) They could hardly see anything through the thick fog.
(b) They could rarely see anything through the thick fog.
(c) They could seldom see anything through the thick fog.
Hardly means that it is difficult to do right now. I can hardly hear you right now. But does not say anything about the situation in general, just about this occurance.
Rarely/Seldom mean that it is difficult to do in general, but does not specifcally say what the situation is right now.
(a) means they have diffciculty seeing right now because of the fog. Because it is a foggy day right now. But it may be clear and bright normally.
(b/c) means they have difficulty seeing. Because we normally have lots of fog round here making it a general difficulty to see things. But it may not neccesarily be a difficulty right now.
The first one is ok for all three though.
1 (a) He hardly complains about anything. He's an optimist.
(b) He rarely complains about anything. He's an optimist.
(c) He seldom complains about anything. He's an optimist.
Complains is not time dependant here, or a series of events such as 'rarely sees'. Here you are talking about his general attitude, not a specific event. Hardly means the same as rarely here.
Complains is an intransitive verb without an object so the diference is probably linked to that.
(Sorry but as a Native speaker I can see the diferences, but may not know the exact reason in terms of English Grammar).