Car- is the Quenya verb for “do, make”, derived from the root √KAR of the same meaning, and was very well established in Tolkien’s mind. ᴱQ. karin “I do, make” dates back all the way to the Qenya Lexicon of the 1910s (QL/45), and appeared regularly in Tolkien’s writings thereafter. Tolkien frequently used car- in examples of conjugating basic verbs, so the inflections of car- are pretty representative of Tolkien’s evolving notations of the Quenya verb system.
The English verb “do” has many specialized functions, such as in the formation of questions like “do you want to go?”. Quenya car- does not share many of those functions. Quenya car- serves as a “generic action” verb, in some sense acting like verbal pronoun, which can be substituted for a more specific verb. For example, in phrases like A carnë ta yallë B (carnë) “A did that as / like B (did)” (PE17/74) or ecuva nin carë sa nöa “I may do that tomorrow” (VT49/20), the verb car- is a placeholder for the specific action done, in the same way that ta and sa is a pronominal placeholder for the action as a noun.
The English verb “do” often requires a generic object like “it”, but that is not the case for Quenya car-: consider English “don’t do it” [with object] vs. Quenya áva carë [without object] (WJ/371) or the Quenya phrase á carë ancárië “try harder” (PE17/94), more literally “✱do [it] with more doing”. When car- has a specific direct object, it generally has the sense “make” or “build”, as in ma caruvalwë ohta “shall we make war” (PE22/161) or i carir quettar ómainen “those who form [make] words with voices” (WJ/391).
Conceptual Development: In The Etymologies of the 1930s Tolkien had ᴹQ. karin “I make, build” under the root ᴹ√KAR {“make, do” >>} “make, build, construct” (Ety/KAR), and in this period kar- was more often glossed “make” rather than “do”, such as in the Quenya Verbal System (QVS) from 1948. It could be that in the 1930s and 40s this verb was more limited in sense than it was earlier and later.
Neo-Quenya: Orondil suggested this verb can probably also be used intransitively for “to act” [= “take action”], especially given the suffix -carë often used as “action”. For a more distinctive verb for “to act, take action”, see [ᴺQ.] carta-.
carnë adj. "red", "scarlet, red" (SA:caran, PE17:154, MC:214, KARÁN - spelt with a k in the two latter sources), not to be confused with the past tense of car- "do, make". Stem carni- as in Carnimírië, Carnistir.