I can only assume something is corrupted on your USB stick. If you want to install a fresh copy of Win 10 via USB, then just google “Windows 10 iso”, and go to the first site in the list and choose “Download tool now” and it will let you create a USB install stick.
No, the batteries aren’t defective. There is a tiny shim/bridge that goes between the MB and the battery connector that often gets lost when replacing the battery. Without it, the battery doesn’t work. See the image here https://www.ebay.com/itm/Microsoft-Surface-Pro-3-Tablet-Good-Battery-Fiber-Connection-Board-See-Details/254202078301?hash=item3b2f9fe45d...
To my way of thinking, MS way over does it with the adhesive they use. It seems they DON”T WANT you to be able to fix your broken Surface devices. It is next to impossible to remove the LCD without shattering it. Why would you want to do the same? I just use a 1/2 inch strip of adhesive in the middle of each side. If you do anything that would knock that loose, it would break the glass anyway. But if I ever need to open the Surface again, it is possible to do it without breaking the LCD.
Both the LCD and battery connectors have a tiny PC board that sits between the MB and the connector. When you disconnect the cable, there is nothing holding them in place and they often come loose and get lost. If the LCD one is missing, nothing shows on the screen. But it will turn on. You can check this by connecting a monitor via the HDMI cable. If the battery one is missing, it won’t charge and won’t turn on unless the power cable is plugged in.