Can I be questioned without my rights getting read to me?

No. The police don't have to read you your Miranda rights unless they question you while you're in police custody and they want to use your testimony against you in court. Many police officers don't bother reading Miranda rights because they have evidence of the crime that is so obvious, they don't need to use your testimony to convict you.

Not having your "Miranda Rights" read merely means that the answers you provided and information derived from them are not admissible. However, if there is sufficient independently or inevitably available evidence then it won't matter.

Miranda only has to be read after someone is arrested (ie. cuffed), and only if there is post-arrest interrogation. Most cops are trained to get everything they need out of your mouth prior to cuffing you, so Miranda rarely applies.

Yes you can be questioned without receiving your Miranda rights. The issue under Miranda is whether the police can use anything you say during the interrogation in a subsequent prosecution against you. Remember that your Miranda rights are only triggered if you are in custody during the police interrogation. You only have Miranda protections if you are being subjected to a custodial interrogation. Therefore if the police have not put you under arrest and are questioning you at your home, the state would argue that all statements you make to the police are freely admissible against you in court. However, if the police put you in the back of a patrol car and then conduct the same interrogation, your defense counsel would argue that the interrogation took place in a custodial setting and any statement you make would be inadmissible unless you were given your Miranda warnings and you freely waived your rights.

A police officer can conduct a limited investigation, including questioning witnesses, without advising people of their rights. This is an extremely fact based situation however, and you need to contact an attorney with experience in criminal defense. A good attorney may be able to get all of your statements suppressed and evidence that was discovered based on those statements if the court finds that it was an unlawful interrogation.