Learn English – Ability in past for positive and negative sentences

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).

In the sentence They gave [object], the object is singular when the group collectively gives a single thing. In your example, They gave their word, the group collectively makes the same promise. In contrast, They gave their lives says that each member of the group devoted or sacrificed their individual lives – even if they shared a common cause.

This is true for all transitive verbs. For example, if a group of comrades make a conference call (or even a series of calls) to a single person, They called their friend. However, if they each make individual calls to separate people, They called their friends.

EDIT: Also note that we don't always pluralize abstract nouns in English. The more abstract the noun, the more likely we are to use it collectively. That's why plural consciousnesses sounds awkward even when talking about multiple minds: We usually think of minds concretely, consciousness in the abstract.

In many cases, you can use a noun either way. Choosing to pluralize or not helps to emphasize whether you mean it concretely or in the abstract. For example, All presidents swear an oath to uphold the Constitution of the United States. This emphasizes that all presidents make an oath of the same nature, even though they all do it individually. They all give their word.

In contrast, we usually write that they devote their lives to upholding the Constitution to emphasize the individual nature of their contributions. You could write that as singular life instead to emphasize the common, abstract nature of their devotion, but we usually don't.