Question: I'm trying to give different privileges configurations for several types of users (Everyone, Privileged, Non Privileged). 

I have tried it using Groups, Global configurations and Queues configurations cannot obtain the output I'm looking for:

* That non privileged users can only comment (not respond) tickets.
* Assign non privileged users as owner of tickets.

So my question:

1. How to configure non privileged user to only comment on ticket cases (not to respond to requester)?
2. How to display & select a non privileged user as owner on ticket creation?

Answer: 
Make two groups: RequestOwners and RequestProcessors.
Grant RPs 'own' and 'comment'
Grant ROs view queue, view ticket details, comment, respond, own

When a request comes in the ROs assign it to an owner or drop it in a queue (RP queue) for RPs to process; when they figure it out they will add a comment and assign it back to an RO or otherwise put it [back] into the ROs queue (ready for response to client).

This should get you the permission profile you want. Privileged doesn't mean what you want - privileged more or less means the user can have specified permissions. Since you want to specify permissions for ROs and RPs you need to make them both privileged users.
Answering my initial questions:

1. How to configure non privileged user to only comment on ticket cases (not to respond to requester)?

Answer= Non privileged users are used to see, comment and respond tickets on the Request Tracker page. To have an inner user that can only comment but not respond the requester of a ticket, the privileges must be carefully specified on queue by the group of user and/or role that the inner user is going to have.

Note: It is very important to strip (clean) all the sections where the privileges can be configured, this include: configurations by Queue, Global configurations (by System -Everyone, Privileged user, Non privileged user-, by Roles, and by User groups). To avoid privileges overlapping.

2. How to display & select a non privileged user as owner on ticket creation?

Answer=Non privileged users cannot be displayed & selected as owners on ticket creation, only privileged users appear and can be selected as owners of a ticket.