I know what hand-spun is and what niputz lishmah is, but what about "lashonos hatzemer?" It seems the Eidoh Chareidis of Jerusalem adheres to this chumroh for tzitzis. All I know is that it's a stage in the wool production process right before spinning, but what exactly is it and where is it mentioned in halacha?
According to what is says here, there are 2 stages in which when making the tzitzit have to have Kavana: The spinning and the interweaving. The stage of lashonos hatzemer, as you said, is the stage before the spinning, and according to some de'ot you need kavana from that stage already
Thank you to Leac and Menachem for their research and helpful answers. A few weeks ago, since asking my question, I just so happened to visit an Alpaca farm, where I came across a lady combing alpaca wool, so of course I asked her for information on wool terminology. I'm still no expert on wool making, but based on her answer I now think lashonot hatzemer refers to "rovings," "slivers" or "battings."
I'd always understood a "tongue of wool" to refer to the wool after it's been combed. Since the wool is long and narrow after it is combed, it is referred to as a tongue, which is also long and narrow. The wool is combed in order to clean it, and to prepare it for spinning into thread or yarn.
I'd never actually seen what it actually looks like until I did some searching on the internet. Turns out there are tons of youtube videos showing how it's done. Here is a blog post where someone describes how they comb wool, with pictures.
In the link provided in the question, niputz is referred to as "carding". Carding is alternative method of preparing the wool for spinning. Here's a youtube video that demonstrates combing and compares it to carding.
So to answer the first question ("What exactly is lashonot hatzemer?"). In order to spin wool into thread, the wool must be prepared. This is done by combing or carding, and the resulting wool is then ready to spin into thread.
As for your second question ("Where is it mentioned in halacha?"), I'm assuming you mean besides the laws of making strings for tziztit, since that was mentioned in the link you provided. I'm not sure of any mention in halachic books, but the first mishna in the second chapter of Tractate Bava Metzia mentions "Leshonot shel Argaman", tongues of purple wool.