Hi Zoe,
It looks like you can speak English well, so it might be easier to understand if you look at these sentences in English. "Ich fürchte mich vor Spinnen" in English would be "I am afraid of spiders." As you see, there is no article in English, either. : ) In this case, because you are not afraid of any certain spiders, and you are afraid of just spiders in general, you don't use an article in the sentence.
"Ich schreibe Protokoll" is "I'm taking minutes" in English. Again, no article. This one is harder to explain why, though. Someone probably started saying it that way a long time ago, and now everyone is used to it and it has become normal. : )
I hope this helps.