The tables you shared explain things like differences of
don't seem to V and
seem not to V or
don't try to V and
try not to V. They sometimes cause drastic meaning change.
Checking that のだ and なのだ cause strong affirmation, or emphasis, let's start with negation.
Think about the below negation patterns of "He is a millionaire".
(1) is simple and easier. The affirmation(なのだ) of negation clause. This just emphasizes the negation clause. It sounds like "He is surely|actually not a millionaire." If the talker of this line was an woman, we could get the 'disappointed' feeling.
(2) is difficult. It has 2 major meanings. This is the negation of affirmation(なのだ). Let me show more examples to explain this case.
(2a) I'm thinking he may be a millionaire.
As you may be surprised, the negative meaning disappeared completely in this case. You could get this as the negation of emphasized affirmation(なのだ) becomes 'guessing'!! なのだ is also used to show a confidence to tell a fact. We could understand this form as negating the confidence.
(2b) He is not a millionaire but the billionaire!
In this case, the negation of strong affirmation(なのだ) becomes partial negation like 'partially right but the point is wrong'. This is often used to excuse something.
「わざとやったんじゃないよ」"I didn't do it on purpose." It acknowledges 'I did' but he/she rather wants to say 'not on purpose'.
Let's take examples "株を買う" "buy stocks". It was hard for me to parse out the difference but finally I got the image below, which is the core model to widely understand the difference.
(3) is simple and easier. The affirmation(なのだ) of past tense clause. This just emphasizes the happening in the past while (4) is difficult because (4) has multiple meanings.
(4a) I missed. I should have bought those stocks.
Along with the image above, we could interpret this sentence like "Once I thought I'm going to buy those stocks". This often shows he/she didn't buy them actually.
(4b) It reminded me to buy those stocks by tomorrow.
The fundamental model would be the same as (4a). "Once I thought I'm going to buy those stocks" but in this time it leads to a different meaning like 'forgot but reminded' according to the context.
Negation and Past tense
(5) is simple. Just emphasizing "He was surely|actually not a student."
In the same way, (6) is 2 ways to interpret. One becomes 'guessing' similar to (2a) meaning like "Once I thought he is a student, so he is a student, right?". The other is 'against the expectation' similar to (4b) like "Once I thought he is a student but actually not".
(7) is simple. Just emphasizing "I surely|actually didn't drink alcohol."
In the same way, (8) is 2 ways to interpret. One is 'regretting' similar to (4a) meaning like "Once I thought I should not drink alcohol but actually did." i.e. "I shouldn't have drunk alcohol". The other becomes 'guessing' and 'reminding' mostly with '?' like "Once I thought I have to drink but I still don't, right?" i.e. "I have to drink alcohol, right?"
The each meaning of the second table you shared (negation of のだ, なのだ) highly depends on the context. Japanese usually uses them separately especially by the intonation.