Translation:It takes one week.
I am not sure, but I suspect it's because "week" doesn't change pronounciation when you start counting them.
With days, each amount/length has its own word. E.g. 二日 (ふつか), on its own, means "a period of 2 days". There's no need to add かん. You can use the same kanji with days, but only if you include の, as in: 二日の間 (ふつかのあいだ) "a span of 2 days".
Words like 二日間 (ふつかかん) and 三日間 (みっかかん) exist, so I don't think your restriction of "only if you include の holds true.
間 (かん) indicates a length of time, a certain period.
It's made up of 'sun' 日 (ひ) inside a 'gate' 門 (もん), which I find helps to remember it. It's like a measurement of time; "the period during which the sun is visible through the gate".
On its own, it reads あいだ, and means "interval", "during", or "within". And since time and space are so similar, あいだ can actually mean "between" (physically) as well.
Bless your kind soul! Separating kanji like that helps me remember them a lot. <3
It's pronounced: いっ which is a variation of いち. Note that the small っ denotes a 促音 (そくおん/sokuon) - it essentially tells you that the consonant that follows it is elongated (germinate consonant). In practice, you will hear a very brief pause between い and しゅう, while the mouth position of し is held before ゅう is pronounced. This 'consonant germination' only occurs to voiceless consonants (/s/,/t/,/p/,/ɕ/,/k/ and etc).