There's nothing wrong with the cited usage. In this precise context, surely and certainly mean exactly the same thing (definitely, unquestionably).
In some other contexts, there's often a tendency to use surely where the speaker is "reasonably" sure of something, but recognises the possibility he might be mistaken. Or even that he already recognises that some unlikely scenario may indeed be the case...
"You're surely not going to refuse to pay the restaurant bill just because there was a fly in the soup!"
...strongly implies that although the speaker thinks refusing to pay is unreasonable, they do in fact think this is what's likely to happen. Using certainly there implies payment will definitely be made - and if necessary the speaker will take steps to impose this outcome.
Note that my example sentence could reasonably be spoken with "question" intonation, and could thus be terminated by a question mark in the written form. This would be far less likely using certainly. It's not that sure is less "definite" than certain - but note what thefreedictionary says...
Sure and certain are frequently used interchangeably; sure, however, is the more subjective term, whereas certain may imply belief based on experience or evidence.
...which in the context of my example means surely can be seen as focusing on the speaker's subjective opinion (he thinks the bill should be paid), where certainly focuses on the speaker's knowledge (that the bill will be paid, regardless of any arguments involving the unwanted fly).
Virtually means "almost (in respect to degree or strength)" or "almost completely".
In your first pair, the difference is very small:
This mission is almost impossible to achieve.
This mission is virtually impossible to achieve.
Here, I think virtually is a stronger choice, so the second sentence simply means the mission is more difficult than the first. Both sentences mean basically the same thing.
Your second pair has a much bigger difference:
He was almost killed in that accident.
He was virtually killed in that accident.
Here, the first sentence can mean either:
He was almost hurt in an accident, but he wasn't hurt at all. (For example, his car almost fell off a cliff, but it didn't fall. He got out safely.)
He was hurt very badly in an accident. He almost died from his injuries.
On the other hand, the second sentence (with virtually) can mean only the second sense. He was hurt badly and was close to dying.
Perhaps a good rule is to imagine that the adjective modified by virtually really is true, but then take a tiny step back:
He was killed in that accident. He's dead.
He was virtually killed in that accident. He's been in the hospital for a month.
Best Answer
Indeed is used when the statement that follows is reaffirming or reinforcing a point that was made earlier.
Surely can have that meaning, but it also frequently implies contradiction or disbelief: "Surely this can't be what he meant." (Note that "Surely", like "obviously", frequently means that the statement which follows is not actually certain or obvious--only that the speaker wishes it were!)
Either of these words might be appropriate in your example sentence, but it would depend on the context. The idiomatic expression "A nod is as good as a wink to a blind horse" means that a small hint will be enough to communicate the intended meaning.
If the previous sentence were:
I would think "Indeed" would make more sense.
If the previous sentence were:
Then I would think "Surely" would be a more appropriate beginning for the sentence.
Both could be followed by an exclamation point, or could not; again, it depends on the context. Neither one would necessarily communicate the meaning of the exclamation point without the punctuation itself.