Can object complements make any difference to sentences?

I'm reading a grammar book, and I have some questions.

A.

• We ate the fish raw.
• I want Sue drunk.
• I prefer the music soft.
• I like coffee black.
• We drank the beer cold.

This type of sentence (Verb + Object + Object Complement) is in frequent use. Then the meanings are the same as the following?

• We ate the fish which was raw.
• We ate the fish while it was raw.
• We ate the raw fish.
• I prefer the soft music.
• I like black coffee.
• We drank the cold beer.
• We drank the beer while it was cold.
• We drank the beer which was cold.

I suspect there will be differences, but I can't catch them.

B.

Another type of sentence is as follows.

• • I know that London is the capital of the U.K. (o)
  • I know London to be the capital of the U.K. (?)

  The book says the latter is not natural, but no reason for it.

• • I believe that the rain is falling. (o)
  • I believe the rain to be falling. (?)

  Same here. The second is said not to be natural.

• • I know Mary to be a Christian.
  • I believe John to be a man of interity.

  But these two are said to be acceptable. Why?

• • I remember him to be tall and lank.
  • I remember him tall and lank.

  Could be there any difference, if any?

• • I find that this chair is comfortable.
  • I find this chair to be comfortable.
  • I find this chair comfortable.

  It says each has a slightly difference nuance, but the contexts are not given. And I don't understand the explanation, perhaps because it was translated word for word into my mother tongue.

• • If you look in the files, you'll find —
    • that she is Mexican. (o)
    • her to be Mexican. (?)
    • her Mexian. (?)

  This is very strange to me. Are all the sentences not acceptable?

C.

I'll type up some more sentences below.

• NBC announced Henry to be the winner.
  vs. "… Henry the winner."
• They report the sea level to be down considerably.
  vs. "… the sea level down considerably."
• He hates gin to be diluted.
  vs. "… gin diluted."
• The police want Bill to be alive.
  vs. "… Bill alive."
• Quick, get in here! Tommy needs his leg [set (o)/to be set (?)].
• Tommy needs his leg [to be set (o)/set (?)] eventually, but let's not rush things.

Solution 1:

An interesting bunch of examples, and correctly grouped.
However, the three groups are not monophyletic. Briefly,

Group A is an example of what linguists call a "rule conspiracy", where a number of independently motivated processes "conspire" to produce a similar surface structure. Georgia Green discussed them in her paper [Green, Georgia M. (1970) 'How Abstract is Surface Structure?' CLS 6, 270-281].

What's come to be called the 'Green Conspiracy' includes such structures as

• I shot him dead.
• I buried him alive.
• I found him alive.
• I need him dead.

et cetera, with very different meanings.

The point, if any, is that there is a limited number of surface structures that English prefers, and there are many more different ways to get from meaning to one of them. I.e, these structures do not represent a single kind of meaning, but rather several. They are all, of course, regular (in much the ways suggested by the OP), but which rule gets used is arbitrary and idiomatic.

EDIT: a little more about Green's paper, which seems to be difficult to find.
This is from a paper by Goldsmith and Huck commenting on the theories involved.

Green (1970), noting that a variety of different semantic structures could be associated with the same surface syntactic construction, argued that there must be a limited set of syntactic “target structures” into which the transformational rules map their representations. The sentences She shot him dead and They buried him alive, she argued, both share the same superficial syntactic structure, but crucially differ semantically as to whether the adjective indicates a pre-existing state or a result. As she pointed out, “natural language syntax is free to utilize mechanisms by which a large and diverse set of logical and semantic relations are somehow squeezed into a small number of surface structures” (Green 1970:277). In that paper, she referred to such mechanisms as “conspiracies.”

Group B is a conflation of several varieties of Raising and Equi,
with different kinds of tensed and untensed complement clauses.

Group C consists of several examples of the rule of to be-Deletion
(p.9 in the Transformation List).

Solution 2:

In “We ate the fish raw.”, the emphasis is on “raw”. That is: the point is that the fish was not cooked. Thus, your first two “same?” sentences have the same meaning (as the original). The third is about eating “the raw fish”; it fails to emphasise the fact that it is raw.

“I want Sue drunk.”, means, “I want Sue to be drunk [viz. in a drunk state].” We say that “the verb “to be” is understood”. (We still say this when the particular sentence leaves out (for instance) “is”, rather than (particularly) “to be”.) Here is an example of the concept: “Tell him his options.”, means, “Tell him what his options are.”

“I like coffee black.”, is the same as, “I like black coffee.”; the word “black” is moved into a position that gives it emphasis.

“I prefer the music soft.”, again moves the word “soft” into a position that emphasises it. This sentence also leaves the verb “to be” understood; it is short for, “I prefer the music to be soft.” (I think these two points are related; someone else might like to comment?)

“We drank the beer cold.”: comments are the same as for the “raw fish” sentence.

— — — — — “I know Mary to be a Christian.”, and, “I believe John to be a man of interity.”, can be taken as examples of how to say such things, and how to use “to be” in that way.

“I believe the rain to be falling.”, is wrong, because that is what rain always does. Actually, “I believe that the rain is falling.”, would also be wrong, for the same reason… unless “the rain” refers to rain that we were expecting, and it is not just that it is not (for instance) rising. One would say, “I believe that [no “the”] rain is falling.”, (or just, “I believe that it is raining.”).

As for London: “I know that… [something].”, is fine. Conversely, the “to be” form is wrong, because your knowledge is that the capital is London, not the other way around. (This deserves a more careful explanation.)

“I remember him to be tall and lank.”, means that he is tall and lank (and that I remember this). “I remember him tall and lank.”, suggests that he is now (for instance) fat.

— — — — —

[I have cut short working on the chair sentences, because it is taking too much time. I think what I have written is okay. For the same reason, I shall leave the “Mexican example”; apologies.]

“I find this chair comfortable.”, is short for, “I find this chair to be comfortable [for me].” (In this particular case, I prefer the latter.)

“I find that this chair is comfortable.”, would be an odd thing to say, completely on its own, because it begs a context. Normally, one would use a sentence like this, in (for example) the following way: “I find that Fords have a soothing ride.” The context there is Ford versus other brands. Back to the chair… it might be that I have a bad back and I am comparing this chair with others… or we might be comparing several chairs — this one is comfortable, even though it looks rather upright.

In other words, that particular way of saying that [about the chair being comfortable] leaves one wondering what would make the chair/you combination not comfortable.

— — — — —

Actually, it should be, “NBC announced the winner to be Henry.”… which means that, in turn, it should be, “… that the winner was Henry.” (Order giving emphasis.)

“He hates gin to be diluted.”, means always — nothing about him drinking it.

“The police want [to have] Bill alive.” — that is, emphasis on “alive”.

“… needs his leg to be set.”, is an odd way of putting it; he does want his leg to be in a “set” state, but the point is that he needs someone to set it. In the same way, “… needs his leg to be set eventually”, is not true; the point of the sentence is that, even though he needs the act of setting his leg to be done, he has to wait.