Deductions & credits

I’m assuming taking into EIC into account makes claiming the student as dependent saves more in tax liability? 

 

Sorry if this is an ignorant question but will EITC  be able to be applied to the parents as well ?

 

What if the student isn’t claimed, is the student able to get EIC or EITC or any other credits or benefits that would make it better to be unclaimed versus claimed?

 

Are there any other tax rules that might help save on taxes in this case? 
@Hal_Al 

 

(if the student spent their unemployment, would that mean they are no longer considered a dependent or just that they can’t be claimed anymore...? How would it affect eligibility for the EIC, AOC, etc? Kiddie tax won’t be affect by this as well would it?)