User with zero privilege able to add/delete security group

Question

I have created a User(user type: member) , I haven't assigned any role's (or) any permission's still the user able to add/delete existing security group's.

Answer 1

No, unless that account owns the group and you have enabled self-service management:

https://learn.microsoft.com/en-us/azure/active-directory/enterprise-users/groups-self-service-management#make-a-group-available-for-user-self-service

and its not a role-assignable group:

https://learn.microsoft.com/en-us/azure/active-directory/enterprise-users/groups-self-service-management#make-a-group-available-for-user-self-service