Q: Car making helicopters/clicking noise when in reverse

Based on the information you provided, there is no obvious connection between the starting circuit fault and the noise that occurs in reverse. Unless the issue is wheel bearing, brake, or axle related your supposition about the noise being from the transmission may be correct. If you request a vehicle noise diagnostic, the responding certified mechanic will pinpoint the origin of the noise for you. As far as the starter, starter motors sometimes develop "bad spots" on the armature of the starter motor. That causes intermittent, unreliable operation just like what you are experiencing. If it happens again, strike the starter with a rubber mallet. If the starter then works, you have diagnosed the issue as a bad starter as the vibration from the strike is often enough to get the armature off the bad spot and the starter will work. If you want the cause of the intermittent starter operation confirmed, please use YourMechanic’s starter diagnostic/replacement service page and the responding certified mechanic will get this taken care of for you. If it turns out the fault is not the starter itself, but instead another issue in the starting electrical circuit, of course the mechanic will still identify and resolve the unreliable staring issue during that same visit. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.