Learn English – “Each one of them” and “Every one of them”

True. But then, if we want to talk about the banana tree's part individually (though all), we use each and not every.

BBC clarifies it-

We tend to use each if we are thinking about members of a group individually, and every if we are thinking of them in total.

Compare the following:

We gave each child who came to the party a present. We handed them out one by one.
We gave every child who came to the party a present We gave them all a present.

Found the exact phrase from the book Hawaiian Heritage Plants where it says each part is usable one or the other way.

You don't need to capitalize the o in the word "one" if it is not the first word of a sentence. The tutorial you watched is correct. The reason the first sentence is ungrammatical is because it is a run-on sentence, which is a very common grammar error. A run-on sentence has two or more parts (clauses), each of which can be a stand-alone sentence. (See how my sentence is similar to the sentences are you asking about?) To avoid making run-on sentences, you need to connect these clauses with conjunctions, such as "and", "or", "but".

So the problem with the first sentence is that "them" is not a relative pronoun and the clause is an independent clause. You need a conjunction to connect the two clauses if you want them both in one sentence.

I have two assignments, and one of them is done.

Or alternatively you need to make them two separate sentences, which means you need to replace the comma with a period.

I have two assignments. One of them is done.

The second sentence reads fine as long as you follow the correct sentence case and change "One" to "one".

I have two assignments, one of which is done.