Diference between ので and　くて/て

Hello! I was studying some japanese grammar and there's something I don't get... (I mean, there's a lot I still don't understand) xD  But in particular, I'm having problems with the use of "node" and "cute" as connectors... I know that both means "because" or "due to", I mean, the reason of something... but what I just don't get is WHICH IS THE DIFFERENCE OR WHEN DO YOU USE EACH ONE?!?!?!?

I leave some samples:
a) cute/de
a.1) 土曜日は　ちょっと　都合が　悪くて、　行けないんです。　
a.2) 手紙を　読んで、　びっくりしました。
a.3) 試験のことが心配で、　寝られませんでした。　

b) node
b.1) まいにち　いぞがしいので、　どこも遊びにいけません。
b.2) びょういんへ　いくので、　5じに　帰っても　いいですか。
b.3) バスが　おくれたので、　学校に　遅刻しました。

any halp?

I think くて/て・で is closer to "and" than "because" and the like.
Certainly, these Japanese words has a sense of "reason," "cause" and whatnot, but my understanding is they can often be translated as "and," e.g.,

a.1) I've got something to do and I can't go out.
a.2) I just read the letter and am surprised.
a.3) I was worried about today's exam and I couldn't sleep well.

ので seems more like "because," "so," "due to" and such. Of course, you can't fully understand foreign language if you stick to translations, but this might help a bit.

Note I'm not a teacher or anything, so I could be totally wrong.

ので literally means "because", its meaning is exactly the same as から, with the exception of ので being more formal.

て-form just connects sentences, although there has to be a connection between the two sentences.

a.1) 土曜日は　ちょっと　都合が　悪いので、　行けないです。
a.3) 試験のことが心配なので、　寝れませんでした。　

b.1) まいにち　いぞがしくて、　どこも遊びにいけません。