Using no-o

Hello,

In school, I've seen the のを~ form.
I understand how to form it...
But I don't understand what does it means and when to use it...

For exemple: 友達に電話するのを忘れました。
I forget to call my friend
But: 来週試験があるのをしっていますか。
Do you know about the next week's test?

So if someone could help me a little bit...
Thanks

It turns a verb into a noun sort of like present participles do in English (call → calling). 友達に電話するを忘れました would not be grammatical because a verb cannot be a direct object, the direct object must be a noun.

Ok, so the first one is I've been forgetting to call my friend...
What about the second one?

Is there a difference between のを and のが?
I've seen the both altogether and don't make a distinction...

ある is the idea if "to exist" (although it would rarely be translated that way), so the second literally means something like "are you aware of the existence of tomorrow's test?"

You should view の as connected to the verb which precedes it, not to the particle which follows. So for example 電話するの means "the action of calling", and it works like a noun.

Ok, so the first one is I've been forgetting to call my friend...

It is not wrong to traslate するのを　verb + ing, but
in this case, it should be,
I've forget calling my friend.

What about the second one?
Do you know about the next week's test?

The meaning of this original sentence were,
Do you know we will have the next week's test.
It should be no problem to change it
Do you know having the next week's test.

今週テストを受けるのを知っていますか？

[来週試験があるの]を知っていますか。
...is the same as the following,
[来週試験があること]を知っていますか。
Do you know [the fact that there is an exam next week].

"の" and "こと" turns the verb into a noun (gerund, in English).

The first one is:
"I forgot [the act of calling my friend]," so, "I forgot calling my friend," which in more natural English would be "I forgot to call my friend."

Is there a difference between のを and のが?
I've seen the both altogether and don't make a distinction...

It's dependent on what comes after the noun phrase, that's all. As someone said, the の is connected to the noun phrase. The particle used after の is in relation to the remainder of the sentence.

E.g.
(コーヒーを飲んでいるの)が好きです｡
I like (to drink coffee).
(ジョンさんが歌っているの)を聞きました｡
I heard (John singing).

Noun phrases can seem complicated but they make Japanese usage less clunky. If you didn't use them you'd end up saying things like: ジョンさんが歌っていました｡ ジョンを聞きました｡

Good luck!

の(no)　is just like "...ing" in English.
電話する make a phonecall
電話するの making a phonecall
電話するのを忘れた I forgot making a phonecall.

の is colloquial and in a literary expression こと(koto) is used.
電話することを忘れた