Does va variability of postures and spontaneous movements correlate with the intelligence of an animal? I was impressed even from a young age seeing the frogs and lizards having their mouths completely shut and opening them only for a reason, not letting them open just because like us. Even more advanced mammals have less spontaneous movements than us. For example usually they won’t touch themselves for no apparent reason like us, or change their postures significantly from the species-typical. Is it related to the intelligence of each animal?

your question is very unclear to me!

I do not think it is likely that postures or spontaneous movements will have much if anything to do with intelligence. Of note defining let alone comparing intelligence between species is fraught with difficulties, to put it mildly. If you search the site (top right hand box) you will see quite a few comments on comparative intelligence.