Does anyone bring down that a Chazan should read the psukim of Kedusha (kadosh kadosh kadosh, baruch, and yimloch) from the ksav to be motzi those people in the tzibur that are still davening shmonah esrei and cannot respond themselves? Mishna Brurah 53:87 quotes the Avudraham who writes that the shaliach tizbbur is called a chazon because he is supposed to look inside the siddur and read. But that's in general and probably not meekev. In terms of reading pesukim to be motzei other people, I didn't find this source, but it sounds right.
I think theres a discussion in the gemara where it says that communities that cannot afford nevi'im scrolls for the haftarah are allowed to read it from a scroll comprised of only nevi'im, and such a scroll isnt really a skav, and although this is a violation of "dvarim shebichtav", still, "eit la'asot La'Hashem hefiru Torasecha". I think the Magen Avraham points out that nowadays with the invention of the printing press, so getting your hands on a full nevi'im isn't so challenging, so we should lichorah use that, and indeed the minhag in many shuls is to use a full Tanach, which has a full copy of that particular week's Navi. But the Chazon Ish (Orach Chaim, Moed, Hilchos Shabbos, Siman 60:11, D"H "Od Katav HaRosh" argues and points out that our printed sfarim dont have a din of a sefer, so there's no maaleh of using a full Tanach instead of the back of a chumash or, lichorah, even a little bar mitzvah boy's pamflet. The minhag in many Hassidic communities is that the whole tzibur reads the haftarah (or megila, besides Esther) to themselves quietly because of the problem of being motzi someone with psukim ba'al peh, while other communities are lenient and rely on our sefarim as not being a violation of dvarim shebichtav. Gra, notably, read shnei mikra from a sefer Torah.
Yashar Koach for your additions.