Is there a way to tell if a root canal is done without x ray?

Not if crown present. If there is a crown on the tooth then probably not possible to tell unless the root canal was done through the crown after the crown was placed. Your best bet if you really have to avoid an x-ray is to look at your dental records. Whoever did the crown most likely made a notation if a root canal has been done.
Done, well, needed? I am not sure what you are asking. Only an x-ray can determine if a rct was already done, and more importantly done well and without any problem or pathology. I am assuming that was the question. Whether or not it is needed, is a different question. That can be determined by x-rays and clinical symptoms.
Not really. Not unless your dentist is clark kent. While you could have an MRI or a cat scan done to see this area of your body, these methods obviously use more radiation then a simple dental xray. Dental xrays use very little radiation, especially digital ones. The risk of the doctor not being able to tell if the root canal is done properly is greater then the risk from the xray. Get the xray done.
Sometimes. Sometimes there is evidence that the tooth had the opening made to do the root canal. However, that really doesn't give any information about how well the root canal was done, or if it healed the original problem. It sounds like you may be interested in avoiding x-rays. This is a situation where it may be difficult to completely avoid it.A digital x-ray has a very low exposure.