There is no definitive answer to your questions, there are so many variables at play in an investigation into a crime like this, not the least of which is whether or not the victim is interested in pressing charges. A good criminal defense attorney in your area may have contact with the precinct that is doing the investigation and may be able to call the police and try and find out the status. If you do not want to go that route, you should call the investigating agency and ask for the shift commander, then ask him who is conducting the investigation and the status of that investigation. Often times, the shift commander will get the criminal investigation moving forward.
[DISCLAIMER- This information is provided as general information only and should not be construed as specific legal advice as this website is not intended to provide anyone with specific legal advice. This attorney is only actively licensed in Illinois. In addition, the answer given above serves for educational purposes only and provides general information and a basic understanding of the applicable law. Anyone using the site expressly consents that there is no attorney client privilege between any person and any attorney responding. No attorney-client relationship is created with the furnishing of this information. This answer should not be used as a substitute for fully discussing the factual nuances of your case with a licensed professional attorney in the state where you are located.]
In Illinois, they have up to three years to charge you with a felony. Realistically, the police will not take that long, but they could take a couple weeks. If you think you are suspect, or that the police may question you, you should not wait to hire an attorney. A good attorney will protect you from questioning and also determine whether you are the focus of the investigation, one of many suspects, or just a witness. If the police get a hold of you without a lawyer, you can be held for 72 hours before they must charge you or let you go.
It is difficult to answer this question, because the police conduct investigations according to their workload, urgency of the crime, and a host of other factors as well. If one believes him or herself to be a possible suspect in an ongoing investigation, it is never a bad idea to consult with an attorney about what to do - in the event that the criminal investigation makes its way to your doorstep. Sometimes, a retainer is given to an attorney for guidance in a situation such as this and then, if an arrest is made, then one can hire that lawyer to represent him/her in court.
The time frame can vary. Typically after the report it will be farmed out to a Detective who will follow up as times allows. If you are a suspect you can expect to be contacted. Do not fall into the trap of thinking that you must talk to the Detective. If you feel you have some exposure, now is the time to consult with an attorney.
There is no "set in stone" answer to your questions. Several factors dictate when the police might actually get around to conducting interviews of potential witnesses and/or suspects. In the interim, you are free to leave the jurisdiction. If you are a potential witness, you could provide your contact information. If you are a potential suspect, you should consult with an experienced criminal defense attorney before you leave the jurisdiction; I provide free consult.