(Zoom the page to see the details of Farsi words.)
1) Note that "بدبختانه" is never used with "خیلی" before it. It's like to say "very unfortunately" in English! Both "بدبختانه" and "متاسفانه" are Farsi adverbs which mean "unfortunately". The latter one is more often used and seems better. Just saying "بدبختانه" or "متاسفانه" is enough for your sentence and has the enough negative meaning.
2) Here is the formula for a useful collocation: مشغول+ مصدر +بودن
You know that in Farsi "مصدر" means infinitive of a verb, for example: انجام دادن (=to do), خوردن (=to eat), رفتن (=to go) etc.
"To do the homework" simply means "انجام دادن تکلیف". Don't add "ی" to the end of "تکلیف (=homework)" when there's no reason for that!!! ^_^ And "to help my mom" means "کمک کردن به مادرم". Note that the preposition for "کمک کردن" is always "به". You have to always use this pattern for that: "کمک کردن به کسی (=to help someone)". In English, "to help" doesn't have a preposition, but some other verbs have, like "to think of/about sth" or "to look at sth" etc. Now you can understand the following collocations:
مشغول انجام دادن تکلیف بودن
مشغول انجام دادن تکالیف دانشگاهم بودن
مشغول کمک کردن به مادرم بودن
(Hint: "تکالیف" is the irregular plural for "تکلیف". It's always in the irregular plural form when you're talking about the university or school homeworks. So never use "تکلیف" again!! ^^ Always use "تکالیف" instead of it!!)
The only remaining thing you need to do is to build your desired verb out of "بودن (=to be)" ; in other words, put it in one of the formulas of the Farsi tenses. I noticed that you're talking about the present time, so "بودن" changes to "هستم". Note that "بودن" is a little different with other Farsi infinitives, and exceptionally changes when it goes to some tenses. For example in the simple present tenses, it changes to "هستم، هستی، هست، هستیم، هستید، هستند (I am, you are, He/she/it is, we are, you are, they are)". As you can see, there's also such a matter in English when using the infinitve "to be"!!! ^_^ Now you can understand the following sentences:
من مشغول انجام دادن تکالیف دانشگاهم هستم
من مشغول کمک کردن به مادرم هستم
You want to combine these two sentencecs into one, so the result is:
من مشغول انجام دادن تکالیف دانشگاهم و کمک کردن به مادرم هستم (=I am busy doing my university's homework and helping my mother.)
This would be your main sentence, and now it's time to add the adverbs or more adjectives to the nouns if you want.
بدبختانه، در چنین وضعی، من مشغول انجام دادن تکالیف دانشگاهم و کمک کردن به مادرم هستم
Yoosh!! ^o^
3) "به همین دلیل، من مدت دو هفته متون خود را تعطیل می کنم" This sentence is understandable to me, but it's not quite right!! it's unusual!!
The word "تعطیل" is only used for shops, restaurants, stadiums, schools, public places etc. when they're closed. Example:
در آغاز سال نو، مدرسه ها در ایران به مدت دو هفته تعطیل هستند.ه (=In the beginning of the new year, schools in Iran are closed for two weeks.) You could have said:
به همین دلیل، من به مدت دوهفته نمی توانم هیچ متنی بنویسم
However this is not the Farsi equivalent for the English sentence that you mentioned in your submission which was "I would like to put off my writings for two weeks".
Whenever you wanna say "I would like" you have to say "من می خواهم (=I want to)" OR "من مایلم (= I'm willing to)". The latter one is more formal and in the movies, it is used by the kings and Queens!! Only use it when you want to talk slightly formally. If you use is when talking to your friends, you've actually said a joke and you'll laught together!! Like this: من مایلم بستنی بخورم، تو چطور؟؟ (I'm willing to eat icecream, what about you??) Hahahaha…… This would be so funny!! Warning: Remember to ask that question in a friendly way, or else, your friend may think you're thinking so proud of yourself like a king and they're like pathetic srevants!!!! Don't say it like an order to your friends. :D
In oder to say "to put off sth" in Farsi, you have to use this collocation: "کاری را کنار گذاشتن (=to give up sth)". The infinitive "کنار گذاشتن" ALONE, has two meanings: A) to put sth aside from the way, center of somewhere etc. ("کنار" means "side of sth") B) to "give up" sth and not doing it anymore. That collocation has only one meaning which is "to give up sth/to put off sth". So you can now understand this:
نوشتن را کنار گذاشتن (=to give up writing).
In order to say "for two weeks" you can say "به مدت دو هفته" OR "برای دو هفته". Consider them as fixed words. Why did you write "خفته" instead of "هفته"?? Do you pronounce it like "خفته"?? That's wrong!! Never say "خ" instead of "ه"! Can you say the English word "half"?? If you can, just add "te" at the end of it and you'll have /hᴂf.te/(=هفته). Easy! ^^ Example:
دانش آموزان معمولا به مدت چهار سال در دبیرستان درس می خوانند.ه (=Students usually study for four years at highschool.)
And finally your sentence is here:
به همین دلیل من می خواهم به مدت دو هفته نوشتن را کنار بگذارم
Ask your questions about the unclear points in my explanation!!
A Farsi proverb: کار را آن کرد که تمام کرد (=The one who finishes his work, has actually done it.)