How do you say: I have been learning Japanese for several months'.
I've come up with '日本語は数ヶ月を習っています。'Or would the word order '数ヶ月に日本語を習っています。' be more precise.
The answer is （私は（implied))日本語を数ヶ月習っています。
Now, first of all, please be reminded 数ヶ月 ( for several months ) is an adverb.
Here is an English site.
Down below near the bottom, there is "Adverbs that don't derive from adjectives" list.
And you can see there, 毎朝,毎日,明日etc etc denoting the time. So likewise these,
数ヶ月 is an adverb and what is modifying is "習っています”． ( = be learning ).
So for the last one, を, the particle. What do you learn? Yes, it is 日本語。
Thus, the answer is 日本語を（object)数か月習っています(verb)。
It conforms with Japanese SOV style. ( Like English, adverbs modify verbs, auxiliary, adjective, right? So, between 日本語を and 習っています, comes the adverb 数ヵ月。
Also, how do I say 'the coming [month]'? Eg 'This coming April I have some time off work.'
The answer is この4月に暫(しばら）く休暇（きゅうか）を取ります。
Now, 休暇（きゅうか）を取ります。 is like as the first one, "take the time off"
So, the grammar is OV. 暫（しばら）く, an adverb, denoting "some time"
このis, in English "This", thus "coming" is inferred.
Here is an English site for Japanese demonstrative adjective
So, 4月, April, に is a particle, denoting, when ( in this case ), thus the answer will be
like "In this April, I am going to take some time off work".