I’m a little confused here. I can say “Tá mé ag foghlaim Gaeilge” for “I am studying” but “Tá sé ag cur báistí” for “It is raining”. Are there general principals for when “cur” gets used in these kinds of constructions?
báisteach (gin. báistí) is “rain”. It is not really a verbal noun (though you can say “tá sé ag báisteach”) but rather a simple noun.
Tá sé ag cur báistí = “Is it at putting rain” = It is raining.
You can use “cur” with any noun that can be put, placed, sowed, planted, set, laid or sent or similar.
But usually not with other verbal nouns.