Who wants to visit whom?
Who does ‘看望，怕，休养生息， 惦念‘？Is that clear from this sentence?


Yes, but the subject is ommitted here, let's restore it:


  (我)好久没有看望萧乾老人了，(我)怕干扰他翻译和写作，(我)怕影响他休养生息，但(我)心里却常惦念着他。


This is verbose indeed, so it's natural to ommit it, especially in the writing at the view of first person.

萧乾老人 is the object of 看望, means the aged named 萧乾.