This thread began with a BIOS upgrade that fortunately did not go wrong. I hope therefore this is the appropriate place to continue with another Dell BIOS upgrade, this time for an Inspiron 15R 5537 laptop. Windows 10 home, 64 bit, Avast Premier, Malwarebytes Premium etc., essentially the same software environment as the desktop just happily upgraded.
The Dell support page offers to scan the computer to find out what drivers (etc.) need updating. That's what I did with the desktop. The same procedure with the laptop yielded 3 recommended driver updates, and a BIOS update from A07 to A10. The A10 is dated 6 February 2018, so is again the "Spectre fix" version appropriate for this computer. The support site said "4 driver updates ready to download and install". For the desktop (XPS 8700) this ran as advertised - all the items were downloaded and all the drivers, but not the BIOS upgrade, were installed automatically. The BIOS upgrade was, understandably, a manual install.
With the laptop things did not go quite so smoothly. The BIOS upgrade module was downloaded first, no problem. As soon as it started to download the first of the 3 drivers, the download crashed. The screen said "download completed" but no automatic install took place and when I looked I found that only the BIOS upgrade module had actually been downloaded. OK, no sweat, I was able to download the 3 driver updates manually,one at a time (took a bit of fiddling, back and forth to be sure I had the designated ones and not anything else) but now I have them all on the laptop HDD. There is the BIOS upgrade (Inspiron_5537_A.10.exe) and 3 driver updates: Chipset_Driver_KV645_WN_188.8.131.520_A02.EXE, Network_Driver_KXHK3_WN32_10.0.0.0_A00.EXE, and Serial_ATA_Driver_923PH_WN_184.108.40.2060_A01.EXE
So am I correct in thinking I should first install the 3 hardware drivers, then use Macrium Reflect to create a bootable rescue disc and an image backup of the entire hard drive, then clear the decks by turning off real-time monitoring apps, WinPatrol, and the AV system, and try to update the BIOS by running the .exe file as I did on the desktop?
FWIW the BIOS upgrade for the desktop was successful even though I did NOT turn off any of the monitoring or AV functions.