Windows Update Problems, 80073712 and 80070436

Computer Type: Laptop
System Manufacturer/Model Number: Asus K52F or Lenovo B51-80
OS: Win 7 x64 Home Premium (and x86 VirtualBox VM)/Win10
CPU: i3 370M/i7 6500U
Motherboard: Asus/Lenovo
Memory: 8GB - finally :)/8GB
Graphics Card: it's an i3, dude!/dual Intel&nVidia
Sound Card: onboard
Monitor(s) Displays: 15.6" built-in
Screen Resolution: 1366x768/1920x1080
PSU: n/a
Hard Drives: 750GB Seagate internal Sundry external drives attached to other computers on the local network 1TB SSD on the Lenovo
Internet Speed: as much as I can get - usually on a dongle/phone, so <1MB/s
Browser: IE11/12/Edge/Chrome/FF(if I must)
Antivirus: MSE/Defender