What's to do? vs. What's to be done?
In order to ask What should be done? or What should we do? using an infinitival clause, you can readily say What's to be done? or What to do?.
(1) What's to do?
But I've heard (1) used in the same sense, which looks similar, at first blush, to either What's to be done? or What to do? but may well be syntactically different from either of those.
(A) Is (1) contemporary and legitimate, albeit less common than the other alternatives?
(B) Here are some of the constructions I think are similar to (1) in that the verb be functions as something other than a linking verb. Please see if they really are similar ones.
(2) What's to eat?
(3) What's to tell?
(4) Who's to blame?
(5) What's not to like?
(6) The guardrail is to prevent vehicles from driving off the road.
Edit: One way to find coherence among all of these is that you can insert the dummy "there" right after "is" and make their meanings more apparent.
Edit: As for (6), however, I'm not quite sure whether the there in The guardrail is there to prevent vehicles from driving off the road. would be a locative adverb (as opposed to here) or the dummy there (as in There's a book on the desk.)
Solution 1:
There are different structures here. I'll use 'structure' to mean 'the syntax informing the actual meaning involved' rather than 'surface structure' (except where I use 'surface structure'!); thus 'He took the dog a bone' and 'He took the dog a walk' have different structures, as do 'Flying1 planes can be dangerous' and 'Flying2 planes can be dangerous' [adjective or gerund?] as Chomsky famously pointed out.
The 'is for the purpose of' (+ -ing form) structure
(6) The guardrail is to prevent vehicles from driving off the road.
(cf [The job of] this switch is to open the motor circuit)
is common in informal registers; other senses for the same surface structure (eg 'The PM is to go to Iraq'; 'Food is not to be eaten in the library') are listed in this 'Grammaring' article and this BBC article.
The expression 'to blame'
(4) Who's to blame?
is a fixed idiomatic one (AHDEL). Rather than 'that we can blame', it means 'guilty / responsible'.
The other expressions are all commonly used in informal (perhaps grading to slang) registers. They can all readily be seen to be punchier equivalents of say 'What is there [that we can] do? / 'What is there to eat? ('to eat' an idiom for 'available to be eaten' which is a passive infinitive).
Of (1), (2), (3) and (5), (2) is very common in informal BrE, while the rest sound distinctly informal AmE to my ears. (1) often sounds marked, either for something approaching desperation or confrontationally. Though it need not be marked, 'What is there still to do?' conveys this better. (3) and (5) can sound confrontational. (2) sounds unmarked.
An older British meaning for 'What's to do?' is 'What's the matter?'