Time to tThink a lLittle

You can also say "A Little Time to Think". Usually we capitalize the nouns of a title.

My girlfriend asked me to accompany her to a funeral, and even though I didn't want to go but, I accepted.

The original sentence sounds a bit too much like 2 separate complete sentences. T

I didn't want her to get home late at night and, alone, so that's why.

When we got there, her co-workers were already there.

To avoid using "there" too much, you can say: "When we got there, her co-workers had already arrived."

She started talking to them andwhile I was silently thinking about life and death. However, I couldn't think much of death, I thoughtinstead thinking to myself that I just wanted to have a long and healthy life, and to have time to do what I like, a. After that, I took my phone out of my pocket and started reading a book.

My girlfriend asked me to accompany her to a funeral, I didn't want to go but accepted.

I didn't want her to get home late at night and alone that's whyto go but I accepted, because I didn't want her to get home alone late at night.

Your original sentence is fine for spoken English!
For written English, I think ordering the sentences this way is clearer.

She started talking to them, and I was silently thinking about life and death,. I couldn't think much of death, I thought to myself that I just wanted to have a long and healthy life and to have time to do what I like, a. After that, I took my phone out of my pocket and started reading a book.

You had a run on sentence, so I turned it into several sentences.

When we left, for the funeral I remember not wanting to go, but now I was feeling thankful because I had time to read, I took advantage of that time to read.

If you just say "When we left", it's unclear if you mean "left home for the funeral" or "left the funeral to go home"

This sentence is also fine in spoken English I think.

My girlfriend asked me to accompany her to a funeral,; I didn't want to go but accepted.

You could write this as either...
My girlfriend asked me to accompany her to a funeral; I didn't want to go but accepted.
or
My girlfriend asked me to accompany her to a funeral. I didn't want to go but accepted.

She started talking to them, and I was silent thinking about life and death,. I couldn't think much of death,. I thought to myself that I just wanted to have a long and healthy life and to have time to do what I like, a. After that, I took my phone out of my pocket and started reading a book.

Make sure to connect independent clauses with ", FANBOYS" conjunctions or periods.
FANBOYS = for, and, nor, but, or, yet, so

When we left, I remember not wanting to go, but now I was feeling thankful because I had time to read,. I took advantage of that time.