case of pronoun changes adverb to/from predicative

Question

First, there are not so many tags, right?

Now, I notice two sentences;

Ему интересно учить русский язык.
Learning Russian is interesting to him.

Он интересно учит русский язык.
He learns Russian interestingly.

I immediately notice that the pronoun Ему is in dative case when интересно is a predicative, but Он is in the nominative case when интересно is an adverb.

Is this just a coincidence?

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It doesn't work so well in the following sentences so maybe in what follows the second sentence is meaningless.

На вечерах вам обычно скучно.
The evenings are usually boring to you.

На вечерах они обычно скучно.
They <spend> the evenings usually boringly.

Where < spend > is obviously not there, so maybe the 2nd sentence doesn't make any sense. Can the second sentence mean anything as written?

I notice that обычно is only an adverb, or the short form of the associated adjective. In all these sentences обычно is treated as an adverb, right?

update So the 2nd sentence here is wrong grammatically, according to @Vitaly.

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Also, in sentence,

Я думаю, им скучно.
I think they are boring.

Скучно is a predicative, right?

Would

Я думаю, они скучно.

mean anything?

update So the 2nd sentence here is wrong grammatically, according to @Vitaly.

Answer 1

The Nominative case is the only thing which makes the noun to be the subject / the doer of an action. Any other case signifies that it's somehow thought to be an object / the passive side.

Here the Dative says to us that it's not "they" who possess some attribute, but rather "they" are posessed / influenced by something.

Они скучны (or скучные) --> They are boring (they have a quality of being boring to other people)
Им скучно --> They feel boring (sort of "the boredom affects them")
Они скучно --> This has no sense unless it's the part of the larger sentence

Answer 2

In English language the same word can change it's role in the sentence. For example, "cut" could be a verb, as in "to cut a tree" It could be a noun "a paper cut", or it could be an adjective as in "cut branches". The role that the word plays in the sentence is determined by its position relative to other words in the sentence.

In Russian language the role of the word is determined by the word itself, i.e. by its suffixes. This role is NOT changed by word's position in a sentence, or other words. For example, "интерес" - a noun "the interest", or "интересный" - an adjective "interesting", or "интересно" - an adverb "interestingly", or "интересовать" - a verb "to interest". There is nothing in the sentence that would change role of those words.

Sometimes (infrequently) one word-form coincides with another. For example, an adverb "интересно учить" is spelled the same as a short singular adjective in neuter gender "это изобретение интересно".

The pattern that you probably noticed (I'm guessing here) in the sentences:

Ему интересно учить русский язык. / [It is] interesting to him to learn Russian.

Он интересно учит русский язык. / He learns Russian interestingly.

Is specifics of subject-less sentences. Because Russian language tends to drop the verb "to be", one gets subject-less sentences. In the first pair of sentences "it is" is dropped in Russian translation. However, "to him" translates into "ему", infinitive "to learn" -> "учить". "Интересно" is an adverb, but in this sentence it could be called a predicative adverb.

In the second pair of sentences "He" translates as "он", the verb "learns" translates into singular third-person "учит". "интересно" is still an adverb.

In a similar manner:

им скучно = [It is] boring to them = they are bored

It is a subject-less sentence, and pronoun is used in Dative case.