This is a very rare usage and cannot be regarded as idiomatic today.
Dare is an odd word—it wanders back and forth between performing as an ordinary lexical verb and as a sort of modal. For instance, it is used with both marked and unmarked infinitives, and it may be used with or without DO-support:
I dare tell you so. ... I dare to tell you so.
How to parse the sentence is not simple. First, it is not a simple sentence. It has two clauses, each with a main verb. The matrix verb is seem, and it is tensed. The rest of the sentence is part of the subordinate infinitive clause, whose main verb is find. But infinitives don't have tense, so it is not a tensed verb.
The logical structure of the actual ...
Peter seems [to have [found his glasses]].
is a catenative construction. Verbs like "seem" and "have" are catenative verbs, a class of verbs defined as those that have a non-finite clause as complement (with a few exclusions, e.g. those where the clause is complement to be in its ascriptive or specifying senses). Examples include:
You seem to like her; I ...
Those now all sound wrong to the modern ear. In contemporary English, that should just be one of:
I never dared to tell you.
I never dared tell you.
I dared never tell you.
Of those, the second may be preferable. Notice how dare can be used without a to-infinitive but just a bare infinitive, where it acts more like a modal verb.
The OED gives only one ...
In this kind of passive voice structures, we have two timeframes: the time of the reporting verb and the time of the reported state or action. The time of the reporting verb will be reflected by the tense of the passive auxiliary "be", and the time of the reported state or action will be reflected by the use of the simple or perfect infinitive.
They say (...
The perfect infinitive means exactly what its name implies: it indicates the perfect tense in contexts when an infinitive is needed.
Your first sentence is fine: “I would like to have lived in the 13th century” is slightly different from “I would like to live in the 13th century”, but both mean basically the same thing. In the former, you are looking at ...
If the perfect infinitive to have known is given as the only correct answer, I strongly suspect that the author of the question is expecting students to apply the rules for reported speech and backshift the tense of the infinitive.
The problem is that a generally held opinion — or one which the speaker wishes were generally held — introduced by “it is said”...
The phrase to have found is not a verb phrase, but a dependent infinitive, which does not have tense. In a limited way, an infinitive can, however, be marked for time relative to the tense of the finite verb, that is, the verb agreeing with the subject. The English infinitive has two forms: present (to go) which indicates more or less concurrent action, and ...
If you say that 'to/modal + have + past participle' is a single construction, you need to explain what makes it different from 'have + past participle'. In other words, you need to explain why the constructions
 to + have + past participle
 modal + have + past participle
are more closely linked with each other than either is with
I understand what you mean with the sentence but it took me some effort. My choice would be:
"It lacks exact references to the book, something about argumentative analysis I would come to learn later in the course."
This tense is called a conditional perfect and is described as "something that might have happened in the past but had not happened at that ...
According to the Cambridge Dictionary it is future perfect simple, and is entirely acceptable.
The reason for this is that future perfect simple is constructed
will/shall + have + the -ed form of the verb
which corresponds to
[I] will have come [to learn]
Those are finite verbs in te present perfect tense, not infinitives. The first has the considering a completed hypothetical action. In the second, the possible considering is ongoing with the planning. – deadrat
"To have been", by itself, as others have noted, means that there was a time in the past that the place was great, and does not say whether the place is still great, or whether that time is gone.
However, in the context of the entire sentence, the passive "It is said" implies distance between the author of the sentence and whoever said it. Likewise, the "to ...
When you need to put a past tense in a context that doesn't permit a finite (inflected) verb, you use "have". The conversion of a non-finite past tense to "have" was proposed by T. R. Hoffman back about 1967 (as I recall, Harvard Computation Lab report NSF-17) and has been explored by McCawley, discussed in his The Syntactic Phenomena of English.
"They say ...
You did overdo it. Tomorrow is not a point in the past, however you stretch the imagination, and you are using something perfect where the point of completion is tomorrow. As noted below, that could happen, but would be totally unrelated to what you meant.
You could render it on-topic, but very strange, by putting 'by' in front of tomorrow, making it ...