“语法成分分析”是外国人先发明的，用于分析外文。

那一套东西有些方法不适合分析中文。

但是这是在教外国人学中文，不是教中国人学中文。

借由外国人熟悉的方法来教中文对于他们来讲更方便一些。

任何语言都有自己的方式表现时空概念。

we also say, 我要吃蛋糕，but it's totaly different from 我要吃蛋糕了.

我要吃蛋糕 means     I want eat some cake

我要吃蛋糕 is a wish, in this case, 要means wish, it's short for 想要.

我要吃蛋糕了 means   i'm going to have a cake.

in this case, 要 means be going to, short for 将要

we need the combain the context to know 要is 将要or 想要

About your second question:

I thought it would be better for beginers to understand, so I added tomorrow to show it's a future event,  and illustrat my point.

Chinese don't say 我将要吃一块蛋糕 , though it's a correct sentense.

we say 我要吃蛋糕了。   when 了 appears in the end of the sentence it usually semantically present the meaning of perfect tense.

了 in this sentence means that I have already decided to eat the cake.

要 in this sentense means I am going to eat the cake.

as I mentioned in the last comment, we need to combain these worlds to understand the tense.

Thanks for the correction.

About your first question:

Mostly, 正在 refers to progressive tense. I couldn't think of an example that 正在is used in other tense.

But here is a sentence that can show the similarity and difference of Chinese and English:

I was eating a piece of cake when the phone rang.

电话响的时候我正在吃蛋糕。

Both language make one more change to present a more complexed tense.

the English changed more worlds, and the Chinese added more character.

Now, here is respective advantage and disadvantage of two language.

In English, we use when to present that the addressor is going to refer a time, and rang indicates that this event happened in the past.

This makes listener easy to understand, and the sentence precise.

In Chinese, 的时候 have the function of refering a time and indicating the event already happened. But we can not tell the tense only from 正在， we need to combain 的时候 and 正在 to pinpoint an tense. in English we don't need the part "I was eating a piece of cake" to know the tense of "the phone rang"

by doing so, Chinese can contain more infromation in less characters. but it might be inconvient for foreign listeners.

我们应该多多种植树木（没错，但植树造林更好）