I think the study guide is wrong and the dictionary you cited is correct: would can be used in the present tense.
A few more examples:
I had hoped that we would be home now.
You wouldn't be thinking of asking her on a date, would you? [present continuous!]
Would you please stop making that noise right now?
The same dictionary entry includes yet more examples of present-tense would.
The example sentence from the CD-ROM actually isn't completely incorrect, as they claim, although normally one would say will be. (I just used would in the present tense again!) Saying would be as in the example expresses less confidence than saying will be. The normal level of confidence for a hope about scientific experiment is expressed by will be.
I recently posted some more about how would differs from will here. I'm sorry it's rather vague and not a rule, and my explanation makes no attempt to be complete, but I think this vagueness is an important part of the language. It's hard to explain the meanings of modal verbs completely because they carry multiple, simultaneous meanings, which can clash with one's intended meaning in an endless number of ways, requiring some odd, inventive solution. For example, you couldn't say I had hoped that we will be home now because will suggests the future while would suggests the past as well as counterfactual imagination. The hope is past and the hoped-for situation is now, so would wins the clash. There is no limit to how many ways these clashes can happen, and there is no simple pattern to the ways people customarily resolve them in different circumstances, so it's very hard for rules to capture the language completely.
For the TOEFL, though, you might be wise to ignore the way the language is really spoken and written and go with the rules they tell you. When people write examinations, they are forced, to some degree, to test knowledge of rules and to ignore subtleties, vague distinctions, and the real flexibility of the language. Considering those things would make the questions too hard to grade.
No and Not are "not" interchangeable in the same way "Yes" and "Is" aren't.
Your examples;
"He is a good teacher" doesn't sound right when we say "He yes a good teacher", likewise "He is not a good teacher" is correct while "He is no a good teacher" is just wrong.
No is a great response where as Not describes the state of something. For example, "JAVA is not a real programming language". Did you ever learn JAVA? No, I did not.
Best Answer
As you say, I am not agree is ungrammatical, because am cannot be followed by a verb in the base (or infinitive form).
I am agreed is grammatical, but fails semantically.
Grammatically it could be the past participle of the verb agree, in which case I am agreed could be a passive: but people can't be the object of agreement, so it doesn't make sense. With a different subject, this is fine: for example, The sale is agreed.
Alternatively, agreed can be an adjective. But this is only used of a group where all the members are in agreement with each other about something: it is not normally used of an individual who is in agreement with somebody else. So we are agreed is fine, but I am agreed is odd.
As simple verbs, I agree and I do not agree_ are grammatical and normal. As you say, nearly all verbs require the helper do to form the negative.