My eternatus I caught just now has 252hp 197special attack and 196 speed timid nature. Does it have max speed I'm not sure

legendaries can't dynamax legitimately

Synchronize doesn't work on Eternatus

You can shorten all of that easily:
Use a Synchronise Pokemon like Ralts as your lead.(Can be dead) The enemy will have the nature of your pokemon.
It's a legendary so IV's don't matter. You'll have to Hypertrain it anyway.
No need to savescum or reset anything.

I tried to give it Dynamax candies but it wouldn't take any. Anyone else have the same experience? I still need to fight the champion if that matters.

How can you check its ivs before even reaching level 4 on the battle tower ?

and thus you can not give it to Dynamax Candies

Eternatus doesn’t Dynamax