If I understood the -ita thing correctly, then ** ece nin caritas is not possible, since it implies "for doing something". In Atanquesta you have (it's Marco speaking about his newly-built house): I nér yen acárielmes túle cenitas. I could translate it like this: "The man we built it for came for seeing it". If it helps, in French I'd add pour before the infinitive, and in Russian it would be чтобы :). I believe, the -ita implies this causativeness, am I wrong?

Yeah, and what's up with i úgerth instead of in úgerth?

+Andre Polykanine the -ita forms are what Tolkien calls a particular infinitive, and they exist so that one can append object suffixes (such as -s and -t) and possessive suffixes to them, which one cannot do with the bare infinitive. So eke nin karitas means exactly the same as eke nin kare sa: "I may/can do it".
I think what you're referring to is the gerund + dative construction, which we find it Cirion's Oath (vanda sina termaruva Elenna·nóreo alcar enyalien "...for the remembering/remembrance of...").

The simple but sad truth is that Tolkien didn’t actually invent languages. He invented a series of interesting but not entirely mutually consistent linguistic paradigms. To call the particular infinitive a “rule” of Quenya is not accurate. It is attested in a couple places in Tolkien’s late writing, but whether it was a “rule” or a “transient experimental idea” is an open (and unfortunately unanswerable) question.

If we want to use Quenya and Sindarin as languages, we are forced to pick and choose for Tolkien’s various ideas to assemble something more consistent and functional. Neo-Quenya and Neo-Sindarin are the best we can do. Or more accurately Neo-Quenyas and Neo-Sindarins, constructed from the various Quenyas and Sindarins (and Qenyas and Noldorins and Gnomishes) that Tolkien invented.

Frankly, given how messy things are, I am astounded at how well we can communicate anything in these “languages”. It’s a testament both to the appeal of Tolkien’s linguistic aesthetics, and of his fans willingness to study and expirement with his ideas.

"f we want to use Quenya and Sindarin as languages, we are forced to pick and choose for Tolkien’s various ideas to assemble something more consistent and functional."
That's exactly what I did in Atanquesta.