Correct, shellac is a secretion of the lac bug.
The main producer is India. It's very labor intensive, involving people collecting the branches on the trees or bushes with the lac bug infestation, havesting the bugs, and then going through various fairly primitive isolation and refining techniques. Shellac is still quite useful today, and it has the advantage of being one of the least toxic protective materials one can use.
As far as I can tell, the main military uses of shellac were for insulation (as stated) but also as a coating for ammunition - to keep the powder dry and corrosion to a minimum. It was also used extensively by the Russians to protect entire rifles from corrosion, from stock to barrel.
Although I don't think trade with India was ever completely cut off during WWII, no doubt it was reduced due to wartime restrictions on shipping. An imported material that could be conserved and recycled at home meant more shipping available for transporting armor, troops, military supplies, and food for a besieged England.
This has been discussed here before, but early 78 needles, back in the days of the acoustic gramophone (Victrola), were meant to be used only once. They were honed to an appropriate shape by the first few abrasive grooves in the record, but by the end of the record they got sharp corners that could damage records if they were re-used. These old shellac 78's contained more abrasive material than later 78's meant to be played on electric phonographs. Some outfits sold needle sharpeners; never seen one nor do I know how well they worked. Victrola introduced a new type of needle, made of fine tungsten wire, which had a small enough diameter that even if worn down would not damage grooves. I've experimented with this type of needle on my grammaphone and noticed that it needs to be periodically honed on an old 78, after which it can play more modern 78's for a while before needing to be honed again. The drawback of the "Tungstone" needle is that the fine wire can easily be bent if the receiver is dropped on the record, at which point the wire must be clipped or a new needle used.
People also used bamboo needles on the old 78's. I understand they had a much softer tone. In fact tone control on old acoustic gramophones was largely a function of what type of needle one chose to use. It all seems rather quaint and awkward today, where we have bass and treble controls, not to mention equalizers and fancy sound processing capabilities, but back then I suppose it was a treat to have any recorded music at all inside one's home.
Before and during WWII record companies were experimenting with different disc materials - including some that had a cardboard core and were claimed to be "unbreakable". Some of these had a lot of background noise and distortion and shellac was generally the standard. Interestingly, hi fi mono phonograph recording was developed for radio transcriptions in the 30's, with special records and recording/playback heads, and some of the techniques developed then were used for the later 33-1/3 hi fi recordings that started becoming more common in the 50's.