I was wandering if a military member married in the state of Illinois is contesting a divorce how log it can take and after how long he can get remarried?
To contest a divorce and predict outcomes from such action will depend on how complex the divorce is in the first place. It really doesn't matter if a party is a veteran or active military in all but a few instances of OCONUS deployment and such.
If there is a lot of property, money, children or other issues that are up for dispute and lawyers are deeply involved, the process can last weeks, months, or more.
If the action is no-fault, as most divorces are these days, and there is little to dispute the divorce can be done in one session of the court. No-fault divorce isn't very complex, the court follows a set pattern each time and parties fill out papers prior to the hearing so a lot of what happens will have already been determined.
I'm not aware of any barriers to remarriage. Once divorced either party is free to remarry should they choose to do that...they're single again.