Could I get drug probation if I go to school out-of-state?

I agree. Post this question in Illinois forum so you can get some Illinois feedback.

How much time will she do

Several factors matter - since it's 2 class D felonies and if it's her first time down - she'll probably do 15-25%, on a four year sentence that...

I was charged with possesion the officer said he saw me stuff drugs between the seat from inside his vehicle i put syringes on f

It's called "constructive possession". You may have a good case for trial. Get a lawyer or apply for a public defender.

How would i be able to get my class c felonies expunged in sealed and get all of my rights back in the state of missouri

You're never getting your convictions expunged and you're never getting your rights back.

Can a class c felony be removed form my record and rights restored?

Probably not. Most expungeable offenses are misdemeanors.

Expungement

Title your motion "Nunc Pro Tunc" and file it. Put in the motion the day the ADA said, then put in the day it should say.

Go to Court and ask for a trial. I would suggest arguing for a motion for acquittal at the close of the city's case - because they won't be able...

Would providing proof of insurance of the car be enough to clear the ticket? Do I need to get an insurance for that vehicle too?

Take a photocopy of each insurance card - both insurance cards - to the clerks office and they will dismiss your ticket.

No. You won't get anything in the mail.

I was caught shoplifting at Walmart. I am a first time offender I have never been in jail or in any trouble. Will I go to jail?

In StL, it will be a probation case. Hire a lawyer OR go to the closest public defenders office and fill out an application.