I would use:
I strongly believe that... or
It is my strong belief that...
If you have a strong set of facts but can't prove it, then you could use:
I understand that... or
It is my understanding that...
These days I would not use assume in any serious context (in the US anyway), due to the now well known reply to its use - What Happens When You Assume
The short answer: go is used when something or someone is leaving or moving away from you.
You: "Please go."
Other: "Okay I'll leave. Bye."
Come is used when something or someone is moving from their position to yours.
You: "Come here."
Other: "I'll be right there."
In this example you are telling another person to move from wherever he/she is and move to where you are.
In the article you quoted, the examples are from a third person's perspective and are in past tense. Here are some examples similar to the ones in the article:
"His friend went to the store the other day to buy some fruit."
His friend is the doer because he/she is the one who went to the store.
"Her dad came over and said hello to Jason last Tuesday"
Her dad is the doer and Jason is the receiver.
Something else I noticed about the article: went and came are used in a slightly more complex way than the way I used them in my examples. In the first sentence, Yolanda may have, but did not necessarily physically move from her location to her mother's location. It can certainly be inferred that for Yolanda to get help from her mother she had to physically go to her mother, but it's less clear than in my examples. The sentence, in black and white, only means that Yolanda sought out help from her mother. Also, I'm not sure I would agree with the article's explanation. If the first sentence is from the mother's viewpoint then why did she refer to herself in the third person? She should have said "Yolanda came to me for help" instead.
TL;DR:
Go and went have different meanings in the article's sentences than in mine. In my sentences, they mean to move from a place to a different place. In their sentences, they mean to get help from someone. The difference is subtle but present.
Best Answer
A plan is more concrete than a dream or wish. Plans succeed, work out or have results.
You could say "The woman points out that this [that the plan would help] would not necessarily be the case."