Which article should I use if I want to say, for example:
Let's discuss/Let's talk about (the) English/Russian grammar.
Is the definite article “the” needed here or not?
The definite article is definitely NOT required, as stated by the previous commenter, and is actually more common and natural without it, i.e. Let's discuss Russian grammar. The use of the definite article here is not incorrect, however it is superfluous and awkward, at least to my ear.
In another context, one would say: I'm having trouble with Russian grammar. If one said the Russian grammar here, it would call to mind the grammar textbook, since this is also called a grammar.
Also note the following: Let's discuss...
The definite article is required as you are talking about the specific grammar of the specific language out of those three grammar
This said, it should be...
Let's discuss or talk about the English grammar.
It can also go without any article if you are talking about English grammar in general. Ah, I just said it!