こき is the masu-stem of the verb こく, and こく should be in any dictionary.
扱く in Kotobank and jisho.org
放く in Kotobank and jisho.org
こき in 嘘こき is masu-stem as a noun.
Note that 扱く and 放く are different words although both are almost always written in hiragana.
Yes, ～はどうですか can be used in several ways.
"How is ～?"
How is he doing recently?
How is Japan? / How do you like Japan? / How is your stay in Japan?
"How/What about ～?" (suggestion, offering)
How about some tea?
How about (going to) Japan? / What about Japan?
"How/What about ～?" (...
Saying 毎日学校に行ってくる implies the "mental point of view" of this sentence is fixated to the speaker's home, but I think that's weird. A sentence like "I go to school every day" is usually used outside one's home, and returning home is not really part of the purpose of this habitual action. Compare this with ママは毎日スーパーでリンゴを買ってくる, which is ...
For your completing enjoying any piece of work (not limited to series), you can simply say [verb]-終わる／終える or 全部 [verb]-る. Verbs are different according to medium, so 読む for books, 見る (formally 視聴する) for audiovisual (TV, video...), and 聞く for audio (songs, radio...). ～しまう indeed partially covers such a usage but not easy to use in this situation.
Here Japanese actually matches English usage quite closely: "teaching 勉強" is simply only one possible sense/meaning of all the kinds of teaching that "teaching モノ" (i.e., teaching in general) could conceivably entail.
"To be honest, [when it comes to teaching] in the sense of teaching academic ...
Is the word "interesting" (or its Japanese counterpart, whatever it is) something you insist upon? It's a word that by definition suggests a positive evaluation. Sure, it doesn't have a "funny ha-ha" kind of connotations but if, for example, someone told you about a sad, tragic or serious event and you responded with "Oh, that's ...
I don't recommend 興味深い either. That's not safe either because it basically means "I'm curious".
Considering how English speaking youtubers say "hmm, interesting", なるほど… or そうでしたか… seem reasonable to me, but if you are somehow not content with those phrases, how about compromising settling for either of them with "勉強になります"?
Based on my limited life experience, what we say idiomatically in such a situation are:
roughly: "I/we owe —'s having been possible to everyone."
roughly: "— were not possible without everyone's help."
Of course, these assume most addressees ...