"It takes ten months."
In a different version of this sentence someone said it's a way of indicating a span of ~ months. 十ヶ月 → a span of 10 months 十月 → october hope it helps!
Looks like "ke" but is pronounced "ka" when written in small font and used to indicate a duration. October would be shuu getsu while 10 months would be shuu ka getsu
I think you meant to write: October would be juu gatsu while 10 months would be juu ka getsu.
Yes, the small ヶ vaguely resembles the upper part of the kanji 箇 (ka), which is a counter for months and places. Today, this abbreviation is the usual character for counting months. It is small, because it could be confused with the kana ケ (ke), which is pronounced differently.
What's the difference between 月間 and ケ月（sorry that ケ should be small, keyboard acting up)?
First of all, to type small ケ, you just type ｘｋｅ (ヶ) on your computer. You would usually put an ｘ in front of some characters to make them small. I most commonly do this with ｘｔｓｕ (っ）.
ヶ is a counter specifically for 月 that is placed before the kanji to make ヶ月. It is required when used to count months and was intended to be used so people could differentiate between months as a time span vs the names of the months of year. For example, 十月 (October) vs 十ヶ月 (10 months).
間 is a counter placed at the end of the kanji used to designate time spans. It is optional for most words. In fact, it's only required for hours (時間). And it's more often used for weeks (週間). This means that you can write months as a time span as either ヶ月間 or ヶ月.
You wrote 月間 which (as far as I'm aware) is only used to talk about month-long events like Black History Month or Breast Cancer Awareness Month.