1) The situation is said to be critical.
"critical" is an adjective. It needs a form of the verb BE (is, are, was, were, been, to be, and son on). For example,
[a] The situation is critical.
[b] The situation is said to be critical.
In [a], "critical" follows a form of the verb BE, notably "is". In [b], the word "said" is placed between "is" and "critical". "said" is not a form of BE, so "to be" is added in order to make "critical" fit the sentence structure.
2) These types of nouns are said to be in the possessive case.
Same holds true here. See 1). "said" blocks the phrase "in the possessive case" from its BE verb ("are"). It's a prepositional phrase in form, but it's an adjective in function. "in the possessive case" describes the word "nouns". Its an adjective, and adjectives need to follow a form of the verb BE, so "to be" is inserted.
3) These trees are not to be found elsewhere.
Same holds true here. See 1) and 2). "found" is an adjective. The word "not" is inserted between "are" and "found". "not" blocks the adjective, so "to be" is inserted to satisfy grammatical constraints. Note, "to be" is the base form of BE. There's no tense. It's bare and that's why it is chosen. It's a connector.