Hi again.
Shiken=test/exam, also I'd write it so that "kara" linked the two parts of the sentence. You CAN do that.
In the first sentence, it should be "Watashi wa kyou hima DEWA/JA NAI", since you need to use the negative form of "hima" which is a -na adjective.
"Ashita, shiken ga arimasu kara, kyou wa, hima dewa/ja nai" (you can omit the "watashi").
In the second sentence, you need to use the past tense, so it should be "Takusan benkyou shimashita kara, shiken wa muzukashikunakatta (the negative past form of muzukashii).
For the third one, use "konya" instead of "kyou no yoru", and "dekakeru" conjugates as "dekakemashou", but apart from that, it's good. You could also put a "desu" after the "yasumi"
"Ashita wa yasumi desu kara, konya dekakemashou."
For the fourth, "haha" is only used for your own mother, so "watashi no" is unnecessary. You need the past tense of "isogashii" (ishogashikatta), "ni" should be replaced with "o", "kanjyou", doesn't exist, it should be "kanojo", and "tasukeru" is incorrectly conjugated. It should be "tasukemashita". Since I'm putting "kara" in the middle, I'm switching "haha" with "kanojo" to make more sense.
"Haha wa ishogashikatta kara, kanojo wo tasukemashita"
For the fifth, again, you'll need to use the past tense for the "I drank" bit. So it should be: "Asa (wa), kouhii wo nomimashita kara, ima (ima=now) kouhii wo nomimasen."
I hope that helps.