The Kage are named after the 'land' they are from, not the small village they live in. The wind kage protects the Land of Wind, the fire kage protects the Land of Fire, etc. You wouldn't expect the leader of a country to only be named after the capital city of that country after all. (Though sentence discussions really are not the right place for this kind of conversation)
"Kazekage" means "Wind Shadow"; the "Kage" "Shadows" of various elements are characters from the popular anime Naruto. The OP was saying how that name finally makes sense to them and it can be used as a mnemonic to help remember element names, not that the word here is 'kazekage'
If I try typing the Hiragana characters on my computer, (Mac) using the Hiragana keyboard, it automatically converts it to this Kanji, which it says is wrong. I type in Roma-ji, and initially it gives the Hiragana, but by the time I have finished typing the word, it is converted to Kanji—so what to do?
https://www.tofugu.com/japanese/how-to-type-in-japanese/ has lots of tips. The keyboard preferences allow some selection, pressing the spacebar give the Kanji, and just clicking after the first letter prevents it converting a combination of Hiragana (just type Romaji) to Kanji. Small letters can be formed by putting an x (or even and l) before the Romaji vowel.
They are also pronounced slightly different. The accent pattern for 神 is called atamadaka, and is characterised by the first syllable being accented, and getting a higher tone, while the accent pattern for 紙 and 髪 are called odaka, which is just about the opposite of atamadaka. In odaka stress pattern, the last syllable receives the stress, and has a high tone.
寒(さむ)い is used for things like weather, areal temperature (i.e. in rooms, buildings, houses, etc.) and atmosphere (including social "atmosphere" - a "cold" joke, a "cold" look).
冷(つめ)たい is used for things you can touch or feel. And by "feel", I also include things you can feel through emotions (i.e words, expressions, vibes, etc.)
寒(さむ)い部屋(へや) - a cold room // 冷(つめ)たい箱(はこ) - a cold ("frosty") box;
寒(さむ)い時期(じき) - a cold season // 冷(つめ)たい腕時計(うでどけい) - a cold ("frosty") watch.
However, having said all that, there are times when they are completely interchangeable:
寒(さむ)い風(かぜ) = 冷(つめ)たい風(かぜ) = cold wind;
寒(さむ)い手(て) = 冷(つめ)たい手(て) = a cold hand.
All in all, I would say 冷(つめ)たい tends to be more unstable in usage than 寒(さむ)い, so it's best to have an instinct on where does which sound better.
"fuu" is an on-yomi reading for the wind kanji 風 This is the reading for it you'll see in most compound words.
風 かぜ is the wind in terms of talking about the weather, but read as "ふう" it can mean "style/appearance/air" or "Wind" in terms of naming the elements. :)
I have no idea if this is accurate but the way I remember wind is Kaze is Kamikaze.
In Heart of Iron 4 the national spirit to get Kamikaze attacks is called Divine Wind so I just remember Kamikaze = Divine Wind Kami =Divine Kaze = Wind
I dont even know if thats what Kamikaze means or not but its how I remember wind now
First of all, there is not one single definition of what a mora is, and it is often dependent upon which language you are talking about. There is also a large overlap between the concept of mora and the concept of syllable. In general, what is considered to be a mora, has to do with the stress pattern of a language, which parts of a word are stressed, and in what way. I'll give one example first, and try to explain afterwards.
In the word "かんじ"(kanji), there are two syllables "かん"(kan) and "じ"(ji), but there are three morae, "か", "ん" and "じ". In Japanese, morae has to do with the pitch stress system of the language, and are the smallest part of a word that can have an individual pitch. In the example above, the pitch can change from one mora to another, but not within one mora.
Syllables have to do with the relation between consonants and vowels. Typically, a syllable consists of a nucleus (usually a vowel, in Japanese always a vowel), a beginning, called an onset, and an end, called the coda, which are usually consonants. A syllable does not have to have an onset and a coda, but it has to have a nucleus. One way to look at it, that I like, is to say that a syllable is the smallest pronounceable part of a word. In the syllable "kan" you have two morae, where one of them also can be a syllable in another context (ka), and one that cannot be a syllable on its own (n). "ka" is easy to pronounce, but "n" in isolation, is not so naturally pronounceable (it's not really hard, but it doesn't feel natural).
I know these are not very precise definitions, but at least this is how I manage the two concepts.