Which one would be grammatically correct?

Question

Alright, so in my book, the sentence written is this,

She thought that the teachers were influencing those who were going to grow and matter in the world

I admit that because the first clause was in past and therefore, the sentence after "that" will also be in past.. But, I have a confusion here. Consider the following sentence,

He told me that he was going to bathroom

He was going to bathroom at that time and therefore, we used "was" in the sentence.. But in the former sentence, it is an opinion of one woman. As of what I know, opinion can't be considered as past and is basically general thing just like the universal facts. Consider the following sentence,

Our teacher told us that earth revolves around the sun

Consider two more sentences,

She thought/was of the opinion that it is good to help the needy.

She thought/was of the opinion that it was good to help the needy.

Now, which one of the above is correct? The former one or the latter one? In my opinion, the former one is correct. Considering all this, shouldn't the first sentence be,

She thought that the teachers influence those who are going to grow and matter in the world

Please share your opinion.

Answer 1

This construction

...were influencing those who were going to matter

places it all in the past. The students being influenced have probably left school and gone on to their adult lives, where some matter and, probably, some don't because of mistakes or bad luck.

...were influencing those who are going to matter

places the influencing in the past, and perhaps present (we don't know), but the students have not yet gone out into the world, so the time when they will matter is still in the future: they are going to matter.

She thought it is good to help

tells us that this is something she told us, in the past. But she made a general, timeless statement: helping is good.

She thought it was good to help

is less clear. This might be just a way to put the whole telling in the completed past, or it might mean that she thought so then but later changed her mind. We don't know.

But, because most people are taught that helping is a good thing (for some it's even a religious duty: zakat), we have a bigger chance of being right if we suppose she hasn't changed her mind, but that the phrasing is only meant to locate the event in the completed past.

teachers influence those who are going to matter

changes the meaning somewhat. Now the influence happens in abstract time --it's not linked to any particular real time, but can be assumed to always happen, so it's happening now with students who have not yet gone into the world.

Answer 2

If someone says something that you want to tell another person, you can report it using direct speech or reported speech.

In reported speech, we usually put the verb in the reported clause back one tense.

Present: "I'm from Spain."

Past: She told me that she was from Spain.

In direct speech we use speech (or quotation) marks to show the exact words the person said.

"I’m hungry."

In the case of

Our teacher told us that earth revolves around the sun

the action hasn't been completed, therefore it remains in the present tense and the same refers to all the other examples you gave.