I came across the use of would for expressing uncertainty. (Article: https://www.englishclub.com/grammar/verbs-modal-would.htm)
Examples from the article:
would for uncertainty
(1) He would seem to be getting better. (less certain than: He seems to be getting better.)
(2) It would appear that I was wrong. (less certain than: It appears that I was wrong.)
According to the examples from the article, does that mean that when using would to express the uncertainty, we can treat it like the would doesn't exist and the main verb is just a present-tense word, but just with less certainty?
So when we use "would" that way, do we use past tense in the noun clause?
Which is correct in the examples below? Present tense or past tense?
Do (3) and (4) mean the same?
Do (5) and (6) mean the same?
(3) He bought a new game yesterday. He would say he wants/wanted to stay at home and play the game today.
(4) He bought a new game yesterday. He might say he wants/wanted to stay at home and play the game today.
(5) He is quite stubborn. He would insist that he is/was not guilty.
(6) He is quite stubborn. He might insist that he is/was not guilty.