Is there any similar rule for when it comes time to use split & stored yeast too?
That comes back to the volume of slurry and the age. A small amount of slurry only, say 10ml really needs a small volume, 200ml would be the max I would go for. If it is less than a month old, then, you could go for 500ml.
Say I have a stubby of around 300ml in the fridge. Can I step this straight up to a 2L starter? Going by the rule above, the actual yeast (sediment?) is probably only going to be about 20ml or so isn't it?
An old starter of 300ml should not be immediately stepped up to 2 litres. The rule of 10's only applies to actively fermenting starters. Old starters need to start small. Because your stubby of starter is probably very clean, you could boil and cool 200ml of wort, open the stubby, pour off the waste beer, wipe the mouth of the bottle with a strong bleach solution, use a sanitised funnel to pour in the fresh wort, wipe the mouth again, fit sanitised bung and airlock and shake gently. Every time you walk past the bench, gently shake the bottle, when it shows signs of fermenting (solid airlock movement, foam, krausen) then step up in 10's.
Do we just discard the liquid from the top of the stubby and use only the sediment as a base for our starter? So in this case, does that mean I have to step up to 200ml, then can step up to 2L.
Yes, you have the correct ideas.
Can stepping up all be done in the same 2L bottle, or do I need to use a smaller bottle with less air space first then transfer to a larger one? In that case it seems all I'd need to do is pour in some more wort?
So long as the 2 litre bottle is well sanitised, yes, you can use the same bottle.
For example, I use yeast from a petri dish. The first step is into a 100ml erlenmeyer flask with 50ml of wort which was pressure cooked with the mouth covered in foil. This means the very first step is into sterile medium plus is carried out as aseptically as I can achieve at home. The transfer is done on a heavily sanitised surface next to a flame, all surfaces are swabbed with a strong bleach solution, hands are washed thoroughly, transfer wire is flamed, breath is held and yeast is removed from petri to erlenmeyer flask. Once this is actively going, it is poured into a 5 litre demijohn with stir bar and stepped up to 500ml, then stepped up to 4 litres. This proceedure has been slowly built up from lots of information on the internet and lots of help and input from many brewers.
For any budding liquid yeast user, have a go with some Coopers. All you need is a bung that will fit the neck of a standard beer bottle. Everything else you should have already. Funnel, saucepan, DME, measuring jugs.
Many people use dried yeast as nutrient, but have spoken to experienced brewers who tell me it is a not very good nutrient. For instance, boiled humans is not a balanced meal for other humans.