Translation:I immediately sent a text message in order to invite them.
Cxu estas la verbon "tekstmesaĝu" ke pluralo? La traduko nur "text a message"
Are you asking: Is the verb? or is the word?
The word tekstmesaĝo is singular. The verb, which here ends in -is, is unnumbered.
The rest of your post… I'm sorry. Mi tute ne komprenas ĝin.
The verb. It's confusing because the translation option only "send a text message" how about making into "send text messages"
I understand that this particular word/phrase is a bit complicated. But lets try to make it easier by breaking it into parts. send is a traditional verb (Esperante: sendi), message is a noun, and (traditionally) so is text. However, in the phrase "Send a text message" text becomes an adjective. But Esperanto has managed to turn that whole phrase into one compound word. "Tekstmesaĝi" which means "To send (a) text message."
But you seem to be asking about the plural form of that concept; "To send many text messages." Am I correct in that? If so you have options; 1) go back to the noun form of the word (tekstmesaĝo) and write "…Sendis plurajn tekstmesaĝojn…" (sent several text messages) or 2) keep the verb form and drop a numerical marker into the phrase "… tekstmesaĝis multfoje (kelkfoje, ofte, ktp) …" (texted many [a couple of] times, often, etc.)
We, the Beta testers, have been suggesting several options to Duolingo about this, and other, words that may cause problems and so far I, myself, have gotten away with translating the above sentence with words like "texted" "sent an IM" and others.
I do hope that this helps. If not, then I hope that you can find the help you need to answer your question.