Te answer to Q#1 is not adequate

Question

The lesson to explain when to use le subjontif or l'indicatif doesn't, in plain language explain the trigger to cause one to use either tense. It needs to more deeply describe when and why each tense is chosen. This, of course, is my opinion as a student.

Jim Jones · Accepted Answer

Bonjour Wanda,
https://french.kwiziq.com/questions/view/can-someone-please-explain-the-subjunctive-to-me
Please have a look at the above link, where there is a comprehensive discussion on the subjunctive mood.
Typically, in the case of the verbs in the lesson you quote, the issue is whether or not "doubt" is being expressed or suggested?
When, for example, penser or croire is negated, there tends to be a sense of doubting the intention of the meaning.
"Do you not think/believe?"
It is often a matter of some form of emotion being expressed --  Wish, desire, doubt, negativity, etc
I hope this helps.
Bonne continuation
Jim

Anne Davies · Answer

I think the lesson you quote is just saying that there’s a group of verbs that trigger the subjunctive when used in a negative sentence but not in a positive one.

For an even more comprehensive guide, this article from French Today is very useful: https://www.frenchtoday.com/blog/french-verb-conjugation/understanding-french-subjunctive/

Lawless’s site has an exhaustive list of triggers: https://www.lawlessfrench.com/subjunctivisor/).

(On a pedantic note: the subjunctive is a mood, not a tense)