Please check to see if I'm correct.

I have to find the complete subject and simple subject in this sentence.

There was one student still taking the exam when the bell rang.
student is the simple subject and there was one student the complete subject
Am I right?

You're right that "student" is the simple subject.

This sentence has reverse sentence order, however, because of "There" at the beginning. The word "was" is a verb, so it cannot be part of the complete subject.

The complete subject is "one student" -- let me know if this doesn't make sense to you.

Yes, that makes since. I have another question. Can I ask it and see if it's right please?

Sure.

So, this one is a little harder for me. But, I'm giving it a shot.

Japanese animation, with its cutting-edge graphics and futuristic plots, has earned many American admirers.

The complete subject is cutting-edge graphics and futuristic plots
and the simple subject is Japanese animation.
Because has is a verb.

Yes, "has" is the verb.

The simple subject is almost always ONE word.

What do you think?

Ok.. So if it's always one word then I think it would be animation? because Japanese animation could be the complete subject right?

Yes.

And "with ... plots" is also describing "animation." What will you do with that?

In sentences with normal word order, you can usually draw a line just before the verb, and then consider that everything before that line is the complete subject and everything after that line is the complete predicate (verb plus its modifiers).

Japanese animation, with its cutting-edge graphics and futuristic plots, | has earned many American admirers.

Sentences not written in normal word order (questions, inverted subject/verb placement, etc.) aren't so clear. Also, sometimes there are adverbs that are placed at the beginning of a sentence, and you have to be aware of them.

http://grammar.ccc.commnet.edu/grammar/subjects.htm

Ohhhh. Ok!!! That makes complete since now!!. Thank you Sooo much.

You're very welcome!!