Translation:loaves of bread
Bread, like water is an uncountable item in English, so "breads" is not really a valid translation. "loaves of bread" or "pieces of bread" or some other qualifier would be necessary.
o pâine - a bread (fem sg indef)
pâinea- the bread fem sg def)
pâini - "breads" / loaves of bread (fem pl indef)
pâinile - the "breads" / the loaves of bread (fem pl def)
I am guessing people are not understanding the correct pronunciation of "â", which has no English equivalent. The Russian letter "ы" is equivalent to "â", but that is also difficult for non-Slavs to pronounce. If you can make this sound correctly, and leave the final "i" sound off of "pâini ", you will get the result you are looking for.
Since there's no option in the flag, I will put it here. 'Breads' is not an English word. Bread is not countable, therefore it will always be bread (singular or plural). I have a piece of bread. I have two loaves of bread. I have some bread. Therefore, 'Bread' should be accepted as a valid answer, and 'Breads' should not.
Breads is an English word, though I don't think it is generally a proper translation for pâini, because, as you say, bread is not countable. The plural, therefore, refers to more than one kind of the thing--sourdough, rye, and pumpernickel are all breads. I like several breads, but I bought several loaves of bread. As I noted below, clearly to someone's consternation, it is like teas (keemun, oolong, matcha) or milks (goat, sheep, cow).
To your examples, the correct translations would be "kinds of bread" and "types of tea". 'Teas' is also not a word. We like to cut out a lot of words from our sentences, to make them faster and easier to say, but those sentences are not grammatically correct.
In the Pacific Northwestern, Southern New England, New York, and Southern Great Lakes dialects of American English, both teas and breads are words that one can see displayed quite often on bakeries and tea shops, both of which I frequent quite often. A quick Google search, for instance, turned up a list of Chicago's best breads from the Chicago Tribune. The word may be more widely used, though, since Wikipedia provides a list of breads at en.wikipedia.org/wiki/List_of_breads. I suspect the word may even be acceptable in the UK, since the British Heart Foundation provides an A-Z of breads here: https://www.bhf.org.uk/heart-matters-magazine/nutrition/cooking-skills/dough/a-to-z-of-breads.
"Breads" could not be an ungrammatical sentence, since it is not a sentence. It could be an unacceptable word, but in fact, though it may not be used wherever you are, it is quite a common word among bakers, foodies, and really the general educated public in a large part of the Anglophone world.
I realize that you may not want to expand the accepted answers, which I understand. You should not be telling people who, while learning Romanian through English, may also be perfecting their English that breads "is not an English word." Such dismissal of a large and influential part of the Anglophone world on a global learning platform can only be seen as arrogance.
I agree with you that 'bread' should have been an acceptable answer (as that is what I wrote too). However, technically speaking, anything in English can actually be made countable or uncountable. "He makes various types of bread" - "Oh, really? Which breads in particular does he like to make?" I agree this sounds a bit contrived, but I think it is possible to say it in place of saying "which different types of bread does he like to make?".
That's a perfect example of some English slang. Sometimes we take out words that we don't deem necessary for the sentence to be coherent. The grammatically correct version of your sentence would be "Which KINDS OF bread in particular does he like to make?" This concept is a really hard one for my English students to grasp, so I'm very familiar with it.
This is not slang. It is a usage of long standing that can be found in official publications in both the United States and the United Kingdom. Of course, the English language does not have a language authority, like the Academie Francaise or the Institutul de Lingvistica al Academiei Romane, so there is no authority that can ultimately decide. Usage makes the authority in English.