She seemed to enjoy seeing my masterpiece on her birthday stream, so I amwas really glad to take the time to draw it.

I am not an artist and not good at drawing, and she is a real artist, so there was no way to impress her with my poor drawing skills.

That’s why I drew her in a special form which no one else would draw.

She seemed to enjoy seeing my masterpiece on her birthday stream, so I am really glad to tak(that) I took the time to draw it.

I am not an artist and not good at drawing, and she is a real artist, so there was no way to impress her with my poor drawing skills.

TarYoshさんはちょっと嘘つきですね。

That’s why I drew her in a special form which no one else probably would drawuse.

頭がいいですね。

I drew a birthdayn illustration for one of my favorite streamers.

It's better to leave the birthday part out since you explain about the streamer's birthday later in the journal.

You also hinted about the birthday in the title, so lets go ahead and avoid some possible redundancy.

She speaks fluent Japanese like a native speaker, no exaggeration, -- zero gaijin accent.

You can use an em dash (--) or an ellipses (...) to make it easier to read.

English has borrowed a lot of Japanese words recently, I hear kids saying 'cosplay' all the time when they mean you are pretending to do something. It's pretty wild that they're already going to put 'senpai' in the Oxford English dictionary.

Sadly, 'gaijin' isn't really something most people will be able to understand.

Last week was her birthday, so I drew a birthdayn illustration for her birthday present.

So the `birthday ~[noun]`, part of "birthday illustration is a noun adjunct.

Using 'birthday illustration` just doesn't quite work for me, others may have a different sense.

With noun adjuncts It's the same as when using phrasal verbs, you have to read/listen to them a lot before you understand how to use them.
Noun adjuncts starting with birthday:
* birthday present
* birthday boy
* birthday blues
...


Some other noun adjuncts:
* toy soldier
* stone wall
* government policy

She seemed to enjoy seeviewing my masterpiece on her birthday stream, so I am really glad to have taken time to draw it.

This time you're usage of the `birthday ~`, noun adjunct in "birthday stream", reads completely naturally.

My corrected version is written in past perfect tense (https://www.englishclub.com/grammar/verb-tenses_past-perfect.htm) to preserve you're word choice.

You can also write it in past simple tense.
She seemed to enjoy viewing my masterpiece on her birthday stream, so I am glad I took the time to draw it.

I am not an artist and I'm not good at drawing, andbut she is a real artist, so there was no way to impress her with my poor drawing skills.

Not that good at drawing eh? I'm not so sure about that, you look pretty good to me.

This is what my drawings look like: 웃

That’s why I drew her in a special form which, one that no one else would drawuse.

She speaks fluent Japanese like a native speaker, without - no exaggeration, zero gaiji - a foreign accent.

"zero gaijin accent" makes sense for those who are somewhat familiar with Japanese, but I feel that for a more general audience, saying "foreign accent" would be more easily understood.

She seemed to enjoy seeing my masterpiece on her birthday stream, so I amwas really glad to takeI took time to draw it.

Since I am not an artist and, I'm not good at drawing, and becaushe is a real artist, so there was no way to impress her with my poor drawing skill.

That’s why I drew her in a special form which no one welse could draw.

She speaks fluent Japanese like a native speaker, no exaggeration, - zero gaijin accent.

This one is hard to punctuate because it's more of a spoken English style than written. This reads most naturally to me.

She seemed to enjoy seeing my masterpiece on her birthday stream, so I am really glad to takI took the time to draw it.

I am not an artist and notnor am I good at drawing, and she is a real artist, so there was no way to really impress her with my poor drawing skill.

That’s why I drew her in a special formunique style which no one would drawelse would use.

Looking at the drawing I think this is the intent of the sentence