Did it disappear in some transitional period or later, when Modern Russian already existed?
The point is the Russian Plusquamperfect hasn't disappeared, it is still used with a bit transformed meaning and it is used with its normal meaning in Russian dialects.
By the 17th century its meaning changed and it began to mean an action which was going to start, but didn't start for some reason:
Я было собрался идти, но передумал.
The typical beginning of the Russian fairy tales,
жили-были, is an example of the Plusquamperfect.
There's a detailed study of the Russian Plusquamperfect.
It didn't. Modern Russian has three tenses (present, past and future), but in addition its verbs are either perfect or imperfect, like "приходить" & "прийти". Example
He was coming to conclusion at that time. == Он тогда приходил к заключению.
Here the verb (приходить) means that process was in making. However
He had come to conclusion at that time. == Он тогда пришел к заключению.
Here the verb (Прийти) means that at time considered in the sentence the result is already achieved.
In short 'perfectness' of verb tense have moved from grammar to vocabulary and is defined not by form of the verb, but by the verb used. The 'perfect' verbs are not full-fledged and do not have some forms 'imperfect' ones have.