Ok, having studied a few classical languages, I think I may be able to help you out here.
The first two sentences you gave were participial phrases ("Asked...", "Squeezed..."). A participle is a so-called "verbal-noun" which means that in different instances it may modify a verb or a noun.
Therefore we say;
I saw the running horse (adjectival participle [modifies a noun]).
Spitting out the food, he said, "No!" (adverbial participle [modifies a verb]).
A participle is therefore a very unique part of speech, because it finds its place by its relation to other words in the sentence. However, I think the real issue you are having with the above, is not just the participles, but there particular usage in these sentences; and it is difficult to answer because of the obscurity of it.
The uses of the participles here are that of an "absolute" sense, and so they don't relate to a specific verb or noun in the sentence, but the WHOLE of the sentence. They kind of stand by themselves grammatically, but give context to the sentence logically.
The sense is really like the following suggests;
Assuming the situation that he was asked, he replied ...
Assuming the situation that it was squeezed, the steamer ...
The reason your second suggestion doesn't gel with native English speakers is because to add a preposition/particle to the beginning specifies the participle as something more than the original sentence does. And the first case does the same, but it sounds acceptable because it is a proper, albeit different use of the participle, and really says more than the first case wants to as well.