The literal translation of the verb "to be" can only be done with the verbs "ser" or "estar", depending on context. In some of your examples it was not translated into any of those two, but in others like "hacer" or "tener". The reason is we are not actually doing a literal translation in such cases, but giving a different sentence that expresses the same idea but from another point of view.
Let's look at your examples one by one.
El océano es azul. (The ocean is blue)
You are describing how the ocean is in terms of color. It is its natural color. If the sea had a different one in a specific point of time, like when he is almost black due to oil spilled on it, you could say "el mar está negro", and not "el mar es negro", because it is not always black.
Estoy enojada. (I am angry)
She uses the verb "estar" and not the verb "ser" because she is not angry all the time, only in a limited period of time. It is a mood that could change.
If you tell a woman "eres linda", that means she's generally cute (linda). On the other hand, if you say "estás linda", it means that she is cute at that moment, and if you consider her always cute, "estás linda" means that at that moment she is more than normal, perhaps because of the way she is dressed, the make-up, etc.
Fue por la lluvia que me mojé. (It was because of the rain that I got wet)
By your comments I see that you already realized it. The word "fue" is in this case conjugation of the verb "ser" and not of the verb "ir", so there is nothing strange about the translation.
Hay pimientos en la nevera. (There are peppers in the refrigerator)
Both "there is" and "there are" are translated into "hay" in indicative mode, and into "haya" in subjunctive, which are conjugated forms of the verb "haber". If we did a literal translation, we should write them as "allí está" or "allí están" respectively. But in Spanish we express those ideas with the verb "haber".
En invierno hace frío. (It's cold in winter)
In the English example you use the verb "to be" because you are describing how the climate is. In the Spanish one you use the verb "hacer" because you are referring to the effect that the climate makes or produces on an individual. We could also say: "El clima es frío en invierno". Here the confusion is due to what I mentioned at the beginning: sometimes, in the different languages, we express the same ideas in different senses, and the same thing happens in the following example.
Tengo 20 años. (I'm 20 years old)
In Spanish, the used verb is "tener = to have" because we say how many years we accumulated. I's like if we had those years, our existence owns them. The way to ask the age would be literally translated into English as "How many years do you have?"
Now let me put another example:
Estoy en el parque. (I'm at the park)
Here we cannot use the verb "ser". The distinction here is no longer due to the period of time, but to that when I mean the place where I am, I must use the verb "estar". "Estar" refers to being located.