Oh, the books are pretty reliable in general, especially the 新完全
マスター series, it's just there might be some points where it'll say, for example, "this grammar pattern can only be used with nouns and adjectives", when it's used all the time with verbs in casual/slang Japanese. So the information is correct enough for taking the test, it just might not match up with real language use by actual Japanese people. Maybe I shouldn't call it "mistakes", so much as a very specific view of how the Japanese language should function. Kinda like how some English teachers think you shouldn't start a sentence with a conjunction, even though people do it all the time. The 新完全
マスター books should be good prep books for you, just make sure you allow enough time to get through them, as they cover a LOT of material.
As far as reading goes, for nonfiction, there's a lot of websites you can use. Japanese Wikipedia and NHK (not the simplified version) or other news sites are pretty good, but really, reading any site in Japanese will be helpful. I'm not too sure about fiction, but I imagine there are public domain works that you might be able to get for free online. Unfortunately, most of the online fiction resources I'm aware of are more appropriate for the lower levels of the JLPT test; you may be able to find other recommendations elsewhere on this forum. But I have found some stuff on https://forum.koohii.com/forum...
before, you may find it helpful. As far as physical books, anything written for teenagers or adults would be good prep; for example, in the lead up to my test, I read several of the Sword Art Online light novels, The Ring, and a few Japanese history and linguistic books that I had previously read in English during college.
CD Japan should be good, I used to order stuff from there all the time. I forgot they did textbooks now too. It looks like they also sell some light novels and other books, that might be a good resource for you to get reading material.