Run Multiple Thread group Simultaneously

Requirement:

Student logins 2000/hr
Teacher logins 1000/hr

If I want to create a test suite for the above requirement and I would like
both teacher and students run simultaneously. How should I approach this? I
have tried the following way but I am not sure If my way of creating script
is making sure both students and teachers are loggin in simultaneously

Test Plan

|- -Student Thread Group
| |
| |--Http Cookie Manager
| |
| |--CSV Data Set Config
| |
| |--Student Login Request Sampler
| | |
| | |--Synchronizing Timer
| | |
| | |--Constant Timer
| | |
| | |--Assertions
| | |
| | |--Summary Report
| |
| |--Student Logout Request Sampler
| |
| |--Summary Report

|- - Teacher Thread Group

|--Http Cookie Manager

|--CSV Data Set Config

|--Teacher Login Request Sampler
| |
| |--Synchronizing Timer
| |
| |--Constant Timer
| |
| |--Assertions
| |
| |--Summary Report

|--Teacher Logout Request Sampler

|- - Summary Report

So,
1) will this test plan run both thread groups simultaneously?
2) Can I just have one Http Cookie manager under Tesplan rather than having
it as child under each Thread groups?
3) Can I have one CSV data set Config under Testplan and read usernames for
both teacher and student ?