Windows update will not work properly

Yes - the Recovery disks will work on any HD (although depending on the manufacturer you may have some work to do with partitioning the diak afterwards, as it may use a fixed partition size for the system/boot partition).

Yes, an image of your current system is always a good backup - so long as it is stored away from the machine so that physical damage to the HD doesn't trash the backup as well. You should test the image as well, to be sure that it works!
 

My Computer

Computer type
Laptop
Computer 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(s)
it's an i3, dude!/dual Intel&nVidia
Sound Card
onboard
Monitor(s) Displays
15.6" built-in
Screen Resolution
1366x768/1920x1080
Hard Drives
750GB Seagate internal
Sundry external drives attached to other computers on the local network
1TB SSD on the Lenovo
PSU
n/a
Internet Speed
as much as I can get - usually on a dongle/phone, so <1MB/s
Antivirus
MSE/Defender
Browser
IE11/12/Edge/Chrome/FF(if I must)
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