I imagine several people here have Casio Protrek triple sensor watches. If you take it to a jeweller or send it back to Casio it costs about £20, which s a quarter the cost of the watch. However, you can buy the four batteries required (SR927W) for about £4.
I have created a tutorial on how to replace them. It's a bit fiddly, but not too difficult. You need a decent jeweller's Philips screwdriver and a pair of tweezers or a very small flat bladed screwdriver. A short bit of wire to reset the watch is also useful.
Chewie I know carrying heavy kit is fine for some children. My son did his bronze last year. He is built like the proverbial brick outdoor convenience as a result of training 5 days a week for his rowing. One of my daughters is doing her bronze this year. I haven't weighed her recently, but she is almost certainly less than 8 stone. She is fit, but I am sure she will really struggle carrying a typical DoE load.
For a very short section a bit of 9mm rope, say 10m would work. This would give you a 5m recoverable abseil. However, don't try and lower yourself hand over hand. On wet rope this is almost certainly going to end badly. You can easily make a temporary harness out of a long sling and krab. Use something like a belay plate as a friction device. You can also use karabiners as a friction device, but the setup isn't straighforward and is easy to get wrong.
However, practice somewhere safe first as it's easy to make a fatal mistake. Regarding anchors looping a sling, or the rope, around a spike is probably the most foolproof method. Unless you have experience I wouldn't recommend using anything like a jammed nut.