This is another question on backshifting.
I looked at other such questions at ELU & ELL, it appears that the general consensus is something like 'if the reported situation still hasn't changed, it's possible to not backshift'.
However after some googling I also see that people tend to think that verbs like thought/knew/promised etc. maybe should always be backshifted, as opposed to said/told etc., because they supposedly refer more to the action of reporting itself, not the reported one.
Also the tense of the reported incident (future in my case) seems to possibly have some impact on correctness in such cases... and maybe reported situations being not common facts, and being dependent on the reporter themselves might have some impact as well...
So basically, which of these sentences are (can be) correct?
(1) Yesterday, he said he will go to the party tomorrow. (probably correct?)
(2) Yesterday, he thought he will go to the party tomorrow.
(3) Yesterday, he knew he will go to the party tomorrow. (and today maybe he's not so sure anymore)
(4) Yesterday, he promised he will go to the party tomorrow.
(5) Yesterday, he didn't know if he will go to the party tomorrow.
Intuitively, judging by all the info I've found so far, I would guess that all of these might be correct; but I'm not sure.
There are, however, even some quotes stating that 'would' might be forbidden in some cases:
If will is the modal in the reported utterance and expresses future time, and if the situation described in the quote still holds true at the time of the indirect report, the will may not be changed to would even though the reporting verb is in the past tense:
Mr. Arden said that a volcanic eruption will occur next year.
This obviously is a dup in some sense; well, I hope in some sense it isn't.