When I was almost 1 year old - в ед. числе. В этом же предложении, если уж "мои родители говоряТ", тогда "My parents say". Далее, здесь же, не думаю что надо использовать прошлое продолженное.
либо так если используем when,
My parents say that when I was almost 1 year old when they gave me pencils and paper for drawing,
I was banging rhytm of the music which I heard lately.
либо так, если не используем:
My parents say that when I was almost 1 year old they gave me pencils and paper for drawing but I banged rhytm of the music which I heard lately.
Because of it - лучше That's why.
I like it because I can do it very well anyway my teachers say it. Это лучше разделить на 2: I like it because I can do it very well. At least my teachers say it.
Ещё подумаю, наверняка не всё))