Last Saturday afternoon, I went to do a blood donation./I went for a blood donation.

My suggestion is quite colloquial in Australia and thus is grammatically sparse, if you don’t want to sound like this do not use it haha.

It was early afternoon, so when I arrived, there was nobody apart ofrom nurses and doctors.

But a bit later, people wasstarted to arrive/were arriving and I was accompanied by other donors.

First of all, when you come in, you must fill in a form with a long list of questions, but it's easy to fill out.

This list will be examined by a doctor who will haveask you some questions about the form/your answers.

Also, they will check you ther blood pressure.

As all was ok, I passed to/As all seemed well, I was passed onto the next room where a nurse was waiting for me to doing the extraction.

All went fine.well.

Now, sometime in the next couple of/few days, somea person will receive my blood.

Some times, I get a message in my phone informing me that a patient haves received my blood.

Last Saturday afternoon, I went to do anate blood donation.

Sounds more natural.

But a bit later, people wasere arriving, and I was accompanied by other donors.

First of all, when you come in, you must fill in a form with a long list of questions, but it's easy to fill out.

This list will be examined by a doctor, who will have you some questions about the form.

Also, they will check you ther blood pressure.

As all was ok, I passed towent to the next room where a nurse was waiting for me to doing the extraction.

Now, in the next few days, some person will receive my blood.

Some times, I get a message in my phone informing me that a patient haves received my blood.

Last Saturday afternoon, I went to do agive blood donation.

Donate blood is correct, but it is usual in the UK to refer to giving blood

I caught a subway towards Hospital Sant Pau station; and yes, there is a station in the same hospital, in a corner.found the department where blood can be given in a corner of the hospital

Where you can give blood is also correct, but it is better to use the passive "where blood can be given"

It was early afternoon, so when I arrived, there was nobody apart ofrom nurses and doctors.

I´m being very pedantic here so forgive me, but for some reason in the UK we usually say "Doctors and Nurses" in that order.

But a bit later, people wasere arriving and I was accompanied by other donors.

First of all, wWhen you first come in, you must fill in a form with a long list of questions, but it's easy to fill.

What you have written is correct, but my correction scans better

This list will be examined by a doctor who will haveask you some questions about the form.

Also, he or she will check you ther blood pressure.

As all was ok, I was passed to next room where a nurse was waiting for me to doing the extractiontake the blood.

Now, in the next days, some persSomeone will receive my blood during the next few days.

Some times, I get a message ion my phone informing me that a patient haves received my blood.