Is it a difference between "I am doing" and "I am going to do"?
Is it a difference when I am talking about something what I have already arranged to do?
"I am leaving tomorrow morning" and "I am going to leave tomorrow morning".

Question

Is it a difference between "I am doing" and "I am going to do"?
Is it a difference when I am talking about something what I have already arranged to do?
"I am leaving tomorrow morning" and "I am going to leave tomorrow morning".

Answer

As long as you add the time, it's clear that this is in the future and so you don't need "going to."  Both of your sentences are 100% correct.

However, your question should have been:

"Is THERE a difference when I am talking about something THAT I have already arranged to do?"

Answer

Big difference!

I am doing = now

I am going to do = not doing yet, but will soon. (Or soon-ish... this is a future form, indicating there's a plan or process underway already.)

Answer

Я иду домой. = I'm going home.
Я пойду домой. = I'm going to go home.

I'm doing ... (doing it right now, in the present)
I'm going to do ... (planning to do something in the future)