Simple subject: days Simple predicate: can make
Rain/fog are objects of the preposition “of”. They act as modifiers of the word “days” Rain/fog are not the of the sentence.
“Dreary ” and “disagreeable” are adjectives modifying “week”.
Consider this:
Two days can make a whole week.
Ask: two days of what? Ans: two days of rain and fog
Ask: can make a whole week what? Ans: can make a whole week dreary and disagreeable.