1) Waze is only running in the background when you leave it that way - tapping home with it open, the notification icon will let you know it's still active. Switching off completely exits the program.
2) Yeah that "right there" thing does get annoying. I'm guessing they do not expect anyone to report something half a mile ahead or so, though the option would be nice where the terrain permits it.
3) I haven't paid too much attention to the "xyz ago" thing, but I believe it's an hour or so just based on occasionally driving back past my own reports in that time frame. However if someone else drives by and clicks "Not there" on the warning pop-up, it will be removed. I admit there are some who do not pay attention to the "incident this distance ahead part and just click not there early while not bothering to repost it. Also, I cannot confirm whether or not each incident type has it's own time frame. I may ask them that Monday morning. Bonus tip: Most of the hazards have a My Lane/Other Lane option. If you want to report something on the other side, click it to switch.
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If it ain't broke, use a sledge hammer.