Agreed. Have reported/queried the insistence on an article in many similar questions. Conversely, "I am trying a new ice cream" was marked wrong, although just "new ice cream" or "the new ice cream" were recommended answers. There are many instances where the article is optional in English. I think: "trying cake" is fine, but so is "trying a new ice cream".
I confirm that the Russian verb "пробовать" (to try, to taste) is derived from the Latin "proba" which was borrowed into Slavic languages centuries ago. In Russian, the noun "проба" has a variety of meanings from "a test of the pen" to "a casting session" to "a hallmark". "Золото высокой пробы", for example, means "high-carat gold". By the way, most Russian verbs whose infinitive ends in -овать are derived from nouns or adjectives that were once borrowed from other languages. For example, the verb рисовать comes from the German root "reiss" and has nothing to do with рис which is rice. Some of those nouns and adjectives have long since come out of use.
Yes - agreed! Interesting and informative. I would not have realised by myself that the infinitive form of the verb is a clue to its origins. And more parallels with English prove/proof. We have "proof" coins, for example - these are now specially produced coins with a high-standard finish (like high-carat gold), but they used to be trial or test coins, before doing a full production run. And we have percentage "proof" alcohol, which means it has been tested and verified as having that alcohol content. I love language!
Well, in Dutch it's "proberen". All too similar for there to be no connection, I think - so probably a common root. Also English "to prove" used to have the meaning: "to test or to try (something)". Hence the saying: "The proof of the pudding is in the eating" - i.e. "You can't tell 'til you've tried it."
That is my preferred choice too, although I don't think to word it differently is wrong. If you are writing a narrative of past events, but using the present tense to make it seem more immediate and alive, you might say: "We try the cake". I can't think of any situation where you'd say it whilst actually trying the cake! But then again, you would have your mouth full anyway, so it would be rude to say anything. ;)
"A cake" can also refer to a dried flat piece of a cow's feces, which is called "коровья лепёшка" in Russian. A muffin or a cupcake is called кекс (the word is derived from "cakes"). A small cake with cream - too small to be shared by two or more persons - is called "пирожное". The word торт refers to a bigger cake, especially a birthday cake. Cookies (in British English, biscuits) and tarts are called "печенья". A tart can also be called тартинка, but the word is rarely used these days. A Swiss roll is called бисквит (not to be confused with a biscuit). American biscuits known as buns in the UK and many other English-speaking countries are called [маленькие круглые] булочки in Russian.
In English, "cake" is the broadest one, including pretty much any sweet baked good that isn't specifically pastry (which would be under the broad category of "pie") or just "bread". A prototypical cake is equivalent to the French "gâteau", if that helps. Technically there's no real line between cakes, muffins, and cupcakes, but the shape of the latter two separates them. Cookies and brownies aren't usually classified as cakes, but they originated as cakes that weren't properly made (sweet, sweet serendipity).
A "torte" /ˈtɔː(r)t/ is a specific kind of denser, richer cake. The word is a bit fancy.
A "tart" is just a small pastry, usually filled with fruit. Not a fancy word, but not exactly common, except in the commercialized PopTart form.
Oh and in English the word "torta" is sometimes used for a Mexican-style sandwich.