Turning off mains water

Draining the whole tank in the loft is a last resort when changing a tap. Usually there are isolation valves in the hot press, and in fact it looks like there might be one under your sink? Have you tried turning that off? In the absence of isolation valves, I'd bung the outlet pipes on the tank rather than drain it down. Draining the loft tank can cause more issues, like airlocks and introduce dirt into the system.

My own experience has taught me not to do plumbing when the HW shops are closed, in case supplies are needed.

Red lever valve on the left looks like it might be on the supply pipe to the bottom of the hot water tank? if so, that'll isolate the hot water. Lever valve at the front could be the isolation valve for cold water, but I can't tell from just a picture of course.

You can buy rubber bungs specifically designed for the purpose In the past I've improvised using a conical plastic door stop inside the finger of a rubber glove 🤣

Pair of mole grips and snap it off. Nothing you can see there is going to unscrew easily. Although the threaded rod the nuts are on will probably unscrew from the monoblock itself.

I have a set of these which I'd use https://www.amazon.co.uk/Rothenberger-80000-Monoblock-Tap-Spanner/dp/B0020281RK/ although I tend to reach for these long handled mole grips first https://www.amazon.co.uk/Long-Nose-Reach-Locking-Pliers/dp/B007P606LK/

No, once there is no supply into the hot water tank, nothing can come out, so isolating the supply to the hot water tank is sufficient. Then when you open the hot tap at the sink, there will still be some water in the pipes, which will drain out. Depending on the pipework configuration, it'll probably help if you open all other hot water taps in the house too. When turning the water back on, leaving the hot taps open will help prevent airlocks. There will be a lot of spluttering, so best not to open them too much.

Did you identify any valve for isolating the cold water feed to the tap?