does not turn off while charging

My 1040 can be turned off during while charging. I used a wall charger and a non-Garmin bundled USB-C cable.

Maybe yours has problem and need to contact Garmin for a repair/replacement?

could very much be related to the charging source. The reason being that the connecting pushes the Garmin into booting, but if you power down while keeping the charger attached it should go and stay off and charging including the percentage on screen. The unit even shuts down completely when 100% is reached.

Is the charging speed faster if the device is turned off? A full charge from 20% takes 4-5 hours. ( USB, Turned on while charging)

I have the same issue. If I completely turn off my Edge 1040 power while on the USB charger, at first it will show charging level. Then it times out and stops charging!!

I don't want to keep the unit on while charging, especially if I'm charging from another battery overnight. 

Mine does the same. Whenever I plug the Solar 1040 (and I have not updated to 17.29 yet) into a wall outlet with Garmin cable, the unit goes straight to main menu. If I turn it off, it should go to showing just the % charge and charging, but it doesn't, it turns off. What I did find is that plugging into my PC, the main menu does not come up, it goes like my old 1030, loading maps etc and then bringing up just the % charge and charging. It has been doing this since I got the device so I think it is more related to charging source. 

Your power brick is outputting too much power.  Try using a smaller one. Garmin isn’t exactly clear what size to use. I just use to one that came with my iPhone. Seems to work fine

What’s a power “brick”??? Nothing like that came with my Solar 1040.

The Power brick you provide yourself. Not included when you purchase your unit.  If you dont have one most people just plug edge unit directly into their computer to charge but that takes forever. If you want to charge it from your electrical outlet at home you need a powet brick. Problem with that is all power bricks output different amounts of power. Too much or too little power the edge wont charge correctly. Too much power could fry your edge unit so try a low powered one. The brick is the part you plug directly into the wall outlet then plug usb into that, then the other end to your edge. Find someone you know with an iphone and try their charging brick.  I use to charge my edge with the power brick my wife uses to charge her samsung phone. The edge would charge but it stayed powered on with the screen on all night. Even if I powered it off it just came back on. Now i use a lower powered iphone brick (the small square white one) and it works properly. I can turn off the edge while its charging. It only shows the battery progress on the screen but the unit itself is off. When its 100% charged everything turns off. Hope that helps you. 

USB-PD over USB-C negotiates the “power” (actually the voltage, the current is controlled by how much the device draws during charging) between the source and device. While some USB power supplies can provide up to 20V, the 1040 only asks for 5V. Unless you have a faulty power supply which isn’t compliant with the standard, what you describe should not happen. I charge my 1040 off an Apple MacBook PSU which can deliver 80W (20V x 4A) but the 1040 only pulls just over 1A at 5V for approx 6W. And I can turn it off during charging BUT I have in the past seen the behaviour described where it turns itself on randomly. Not sure if I was using this charger at that time)

This it it now, just tested again

It’s almost fully charged so current has dipped to under 0.5A