grammar - Confusion between causatives and intransitive-transitive

I read the answer to this question

How different is 冷やかす from 冷やす? And 散らかす from 散らす?

but somehow wasn't satisfied.

1. 
   

   What's the difference between the 2 causative forms ～す and ～せる, e.g. 待たす and 待たせる?

   
   


2. 
   

   Usually the せる form seems more common to me, but for some verbs, they both seem equally common, e.g. 聞かす and 聞かせる. Is that because the 聞かす I'm thinking of is not really a causative, but a transitive partner-word of 聞く?

   
   


3. 
   
   

   The linked question lists a similar, but un-productive form, ～かす. Not the k from the stem, as in 聞かす, but a k in the suffix. 冷える→冷やかす, 散る→散らかす, やる→やらかす, おびえる→おびやかす. Are these fossilized instances of an archaic productive form, and does it have anything to do with causative?

   
   

Answer

[1] The causative affix -(s)ase- (your せる) is productive and can be used either as let-causative or make-causative.

太郎に音楽を聞かせる
'let Taro listen to music'
'make Taro listen to music'

The causative affix-as- (your す) is not productive, and can only mean make-causative.

太郎に音楽を聞かす
'make Taro listen to music'

[2] 聞く is already transitive.

[3] At least, you can extract the morpheme, so it probably was productive until some point. They are changing intransitives into transitives, not causatives.