今天我打算去我朋友的家。

your sentence is grammatically correct
but 我朋友家 is more natural than 我朋友的家.

我也有很多工作，加上我开始了念硕士，从而我有空了，所以我有空的时间不太多。

我有空不太多 sounds a little unnatural.
the following sentences are better:
我不太有空（I'm not very free）
我有空的时间不太多（My free time is not much）

but in this sentence, changing "我有空不太多" to "我不太有空 / 我有空的时间不太多" directly would be a problem, because you used "从而".

"从而" can be translated as "thereby; thus; consequently; with the result that."
But the sentence with "从而" requires the coordination of the two clauses in terms of predicate type and tense, i.e., either both are action verb-centered narrative clauses, or both are judgmental clauses formed by 是(is), 成为(becomes), etc.
So the following sentences are strange:
我开始念硕士了，从而不太有空。(I started my master's degree, 从而(so) I'm not very free.)
我开始念硕士了，从而我有空的时间不太多。（I started my master's degree, 从而(so) my free time is not much.)

Personally, I have two solutions.

One is to simply change 从而 to 所以(so).
Because the word 所以 is not subject to the rule above.
so you can say:
我开始念硕士了，*所以*我不太有空。(I started my master's degree, 所以(so) I'm not very free.)
我开始念硕士了，*所以*我有空的时间不太多。（I started my master's degree, 所以(so) my free time is not much.)

The other solution is a little more complicated
Let's keep the word '从而' , and turn the sentences ("我不太有空 / 我有空的时间不太多") into a verb-centered sentence like the previous one（"我开始念硕士了"）.
You can use the following sentences as needed:
1. 我开始念硕士了，从而失去了很多空闲时间。(I started my master's degree, so I lost a lot of free time)
2. 我开始念硕士了，从而新增了很多工作。(I started my master's degree, which added a lot of work)
3. 我开始念硕士了，从而变成了一个忙碌的人。(I started my master's degree, so I turned into a busy person)

虽然她是我最好的朋友，但是这个月我这们只见了一次面了而已。

我真的想念她，想极了！

or
我真的想念她！
我真的非常想念她！
-------
“我真的想念她，想极了！“ means "I really miss her, I miss her so much!"

我觉得人们长大的以后，跟朋友见面去玩太难了！

现在我正坐在坐着地铁上写这篇文章。

我正在坐着地铁 sounds a bit unnatural in writing.
我正在坐地铁 is better
if you want to say "I am taking the subway while writing this article", that is, combine the two sentence "我正在坐地铁" and "我正在写这篇文章",
you can use the following sentences:
1. 现在我写这篇文章的时候，正在坐地铁。（Now when I write this article, I am taking the subway.）
2. 现在我正（坐）在地铁上写这篇文章。（Now I am writing this article on the subway.）

ps. Both of the above sentences are somewhat emphatic in the sense that "I'm taking the subway now" / "I'm still riding the subway as I write this." I am not so sure that my poor translation in parentheses conveys this emphasis.
If you don't want to emphasize this point, you can say：
现在我正坐着地铁，写下这篇文章。（Now I'm sitting on the subway and writing this article.）

她住的地方离我家不远，只需要坐十五分钟地铁就能到她家。

"只要……就（能）……" is one of the more commonly used collocation.
I think it's perfect that you used this collocation here.

明天我只有一位客户，然后我终于会能在家休息休息一会儿。

我也有很多工作，加上我开始了念硕士，从而我有空不太多所以我不太有空。

congrats on your new adventure!

虽然她是我最好的朋友，但这个月我这们只见了一次面了而已。

trying to put “了” after the verb when using past tenses.

我真的想念她极了！

我觉得人们长大的以后，跟朋友见面去玩太难了！

I agree, people have loads of things to deal with

现在我正在坐着地铁写，写下这篇文章。

明天我只有一位客户，然后我终于会能在家休息休息一会儿。