2.
2- She was warned that was forbidden walking through the house.
She was warned that walking through the house was borbidden
Is it OK She was warned that it was forbidden walking through the house?
She was warned that it was forbidden to walk through the house. This sounds the best to me.
3.
The way #3 is written by the student is also correct. The student is showing that the key belongs to the garden gate.
6.
Is wordy...
6- I’m sorry for still hadn’t written with news, but I’m very busy here.
I ´m sorry for not having written telling you the news, but I ´m very busy here
Sarah ´s: I ´m sorry for not having written with news/written to tell you the news, but I ´m very busy here
"[H]aving written" and is not a tense, aspect, or modal which I am familiar other than someone trying to sound pretentious.
I ´m sorry that I hadn ´t written with news, but I ´m very busy here.
Just need to change the "for" for "that"
7.
Despite the difficulties, I’m loving this experience in Canada. Only I can put into practice the English that I learned in Brazil probably worth the trip.
Despite the difficulties, I loved my experience in Canada. Only I can put into practice the English that I had learned in Brazil. It was worth the trip.
or
Despite the difficulties, I am loving my experience in Canada. I can finally put my English, that I learned in Brazil, to use. It is worth the trip.
Keep the tenses in past throughout the passage.
8.
What is more difficult for my adaptation here is the weather where often the temperature reaches below zero.
What is more difficult for my adaptation here is the weather because the temperature often reaches below zero.
My adaptation to the weather was (is) the most difficult aspect of living there (or here) . In Canada, the temperature often drops below zero.
Temperature doesn ´t reach zero it drops. Reach has an upward connotation.
11.
11- Recently was born a boy, John, who has only five months.
Recently a boy was born, John, who is only five months
Is it OK, Recently a boy has been born, John, who is only five months
This is redundant...Recently and only five months don ´t mesh at all.
The baby, John, was born five months ago.
Hope you don ´t mind more corrections!