LEGEND:

X - Correction

O - Suggestion

On my profession I am a mechanical-engineer ==> I am a mechanical engineer

and I hope to have found find a job on related to my profession when I will arrive in Australia.

==> and I hope to find a job related to my profession when I arrive in Australia.

For this is why I need to study English. ==> This is why I need to study English.

Hello!
I recently studied English  I want to immigrate to Australia and I need to know the language in order to be issued an immigration visa.

On my profession I am mechanical-engineer and I hope to have found job on my profession when I will arrive in Australia. For this I need to study English.

LEGEND:

Red - Corrections

Blue - Better option

First notebook entry: Introducing myself

Hello!

I study English not long ago. - I studied English not long ago. I recently studied English.

I want to have emigrated in Australia and I need knowledge of this language for be
given emigration visa to me. - I want to immigrate to Australia and I need knowledge of the language to be given immigration visa. I want to immigrate to Australia and I need to know the language in order to be issued an immigration visa.

Note: If you are going from/out of a country, you say emigrate. If you're going to a country, you say immigrate. I assumed that you are going to Australia from your home country, so you will immigrate to Australia.

Example: If I am going to Korea from the Philippines, I would say either:

I immigrated to Korea from the Philippines OR I emigrated from the Philippines to Korea

^^