Which part of speech? ударяв, ударявши

Question

• Question 1:

Forms like these (Verbal Adverb) "ударяв, ударявши" are often listed for verbs on викисловарь but i've never seen them in a grammar book.

For example, разделяв, разделявши делав, делавши and so on

I'm aware that perfective verbs have these forms—сделав, ударив, разделив and so on, which basically mean "having done X".

But what does it mean when an imperfective verb has this form? Is it just an old form? Does it mean something like "having been saying, doing x"

• Question 2:

And what about this form делённый, from делить. As far as I know, only perfective verbs can form these structures—e.g., разделённый итд

When should I expect to see imperfective verbs with this form (Past Passive Participle)

Answer 1

But what does it mean when an imperfective verb has this form? Is it just an old form?

Well, mostly yes. These forms are normal for perfective verbs. For imperfective ones they rather belong to XIX century. Basically, you should use imperfective in present tense only (e.g. "делая"), switching to perfective if past tense required (e.g. "сделав" or "сделавши").

And what about this form делённый, from делить.

It's a passive participle.

As far as I know, only perfective verbs can form these structures

No, imperfective verbs can do it too.

When should I expect to see imperfective verbs with this form (Past Passive Participle)

It is a question about differentiating between participles and adjectives. Sometimes it's a problem even for native speakers. Roughly saying, participle is a "verb-thing"; that's, if a sentence is about action, it's a participle, if it's about quality, it's an adjective. The most common sign of the former is an existence of dependent words. I.e. "белённый известью потолок" is participle; "белёный потолок" is adjective (note different spelling).

To say it short, past passive participle is "almost" an adjective.

Answer 2

But what does it mean when an imperfective verb has this form? Is it just an old form? Does it mean something like "having been saying, doing x"

Usually you can replace them with a present form. While according to the most purist points of view that might be considered a misuse, it's pretty acceptable almost everywhere.

Both these forms are equally acceptable:

Делав свою работу, он останавливался каждые полчаса.

Делая свою работу, он останавливался каждые полчаса.

However, in some cases both past and imperfective are required grammatically. For instance:

Никогда не делав такой работы, он не знал, с чего начать.

In Russian, никогда has nuances in meaning depending on the tense:

• Никогда не делал means "I never did this before (though I might do that in future)"

• Никогда не делаю means "I never do this (didn't do before and not going to)"

• Никогда не сделаю means "I will never do this (though I might have done this before)".

So in the example above, both imperfective and past are required to give the sentence the right (first) meaning.