A new economic recession has set in for that country.
I know "set in" means "start". My question is: Is "set in for" a phrase?
No, the group of words “set in for” is not a phrase. Here “for” is used as a preposition. Besides, the meaning of “set in” is not start. It means: Enter a particular state and/or get established. Winter has perfectly set in. The Sun set in the West.
We can say "set to work". But in Random Dictionary there is "set about work". Does it mean the second phrase has been accepted?
“Set to work” is not acceptable. Set about work is acceptable, because “set about” means:
to begin an action.
We went along a road that led down into a valley, about a mile out of town, where there was a pond. I think the underlined parts are attributes. Is that right?
Yes, they qualify a noun ‘valley” in the preceding sentence.