How do i capture theriari and is there a way to see quest
There are two ways of getting new Theriari, one is by dropping their Primers after defeating them (the rate is 10%), and another one is by collecting their data and going to Dr. Todd's lab (each Theriari gives 20% data when defeated, so you'd need to defeat 5 Theriari to get one of them).
The quest log isn't ready yet, though. It's planned for future versions.