1. Shows me my current position as an OS grid reference (easy).
2. Records and stores a track of where I've walked (easy).
3. Does the above in an extremely power-efficient manner so that the battery lasts several days (probably very difficult).
You dont mention cost / price.
The SatMap Active 10 is colour and works with OS maps, you can choose map ref, Lat/Long or postcode.
You can choose imperial or metric heights / distances.
Gives a 'snail trail' showing where you have walked and gives a 'reverse tral' option
You can save the 'trail' and make it a 'track'
In standard 'full power mode' the my battery lasts 16 hours continuous use.
There are various 'power save options' that will give you up to 100 hours use.
From the manual :
Various power modes for extended battery life
Hibernate mode (100 – 120 hrs)
Advanced Power mode (16 – 24 hrs)
Normal Power mode (8-12 hrs)
Custom Microsoft CE operating system
8.7cm / 3.5 in LCD TFT colour screen (320 x 240 pixels) with variable backlight control
Day/night visible screen with red backlight option for night use
Accuracy down to 2 meters.
Integrated 18mm patch antenna
Price about £70 (secondhand) + various map options from 1:50,000, to 1:25,000, to 1:10,000 for either 'parts' of GB up to 'Whole of GB'