OK so the first thing to get your head around is how breastmilk supply and demand works. Breasts are not like bottles that fill up, have a specific amount and then get emptied and fill up again.
There is a bit of hormonal stuff going on, but essentially the most important thing to know is that milk is being made all the time at the rate of a sort of trickle. This milk collects in the milk ducts. When you have a lot of it, you will "feel full" - heavy, engorged, uncomfortable and possibly leaking.
When you get letdown, which can happen due to your baby sucking, thinking about your baby, the baby crying (any baby crying), you feeling emotional, or it being about the time your baby usually feeds, the flow of milk increases and if you're pumping or feeding, you'll get a faster output. If you're not pumping or feeding at the time, you'll feel a weird sort of draw in your boobs a bit like the feeling of suddenly really needing to go for a wee, and you might leak a bit (Don't worry, the random things that set letdown off are much more sensitive in the newborn period and do calm down).
When your milk ducts are full, either of collected milk or from letdowns, your body produces a hormone that essentially says "Calm down with all these letdowns - we're making too much milk". If you remove the milk at this time, then your body gets the message OK - yep - this was right, make this much milk. But it's not like your breasts are going "OK - baby usually feeds at 9am - commence dump of 5oz breastmilk into this breast immediately". It's more fluid than that, like a mountain stream with occasional rushes from rainfall.
So it's not possible to run out of milk during a feed. As long as the baby is attached, they will be getting milk. The difference is that at the beginning of the feed with a fresh letdown and/or a store of collected milk, the flow is very fast. After this initial gush of milk, they can still feed for longer and the flow will be present but it will be slower. It never really runs out. If you're pumping, you will find that it does "run out" after a short while because when pumping you can only really access a fresh letdown and the stored milk. Breastfed babies sometimes want to stay at the breast for a really long time, much longer than you would pump or bottle feed for. If you don't need to put them down, then I would recommend to let them do this, because they are getting milk which is good for them and also good for establishing a milk supply. But if you do need to stop and do something else, it's OK to take them off once they reach the faster, more "nibbly" and loose sort of feeding, you'll get to know this - the baby might not be happy about it, though. (Some seem more OK with this than others). Breastfeeding especially in the beginning can look a lot different from bottle feeding. It may not be clear exactly where a feed has begun or ended, you don't get the same discrete/clear start and end you do with bottle feeding. And this is OK, but it can feel a bit confusing or haphazard if you're used to having had a clearer pattern with feeding where you know the baby is likely to want to feed every however many hours. With breastfeeding, if they are hungry you can just put them to the breast again, whether it has been a few hours or a few minutes.
With that said, your questions:
- Pumping - there are as many reasons to do it as there are mothers. Some mothers never pump at all. It's not necessary to pump if you don't want to. Most people pump either to get breastmilk into a bottle so that somebody else can feed it, or perhaps if the baby is having difficulty breastfeeding or needs to be tube fed, or to remove milk from their boobs in order to give the message "please make more milk". Perhaps if they have missed a feed or are separated from their baby or they just want to increase supply.
- That routine for using pumped milk sounds fine
- As explained there is not necessarily "milk in your breasts" just because your baby is hungry at that time. Most of the milk the baby drinks is made to order as they are drinking it. So it just depends. If you are having somebody give a bottle so that you can sleep, it wouldn't make sense to wake up and pump. But if you are having somebody give bottles because you are away for a few hours, it might be a good idea to pump at least once or twice within that time in order to keep your supply up. But you probably don't need to pump as many times as the baby feeds. For example during an 8 hour work day, pumping once or twice may be fine. Also, with UK maternity leave you will probably not need to pump at work - this is more applicable to the US where mothers go back to work after a few weeks.
- When my baby was in NICU and I needed to pump I was told sterilising once in 24 hours is fine and just to keep it in the fridge otherwise. You can also get these little breastmilk storage bags, which are pre-sterilised, you just fold the opening over the bottle neck, screw bottle to pump, pump, take bottle off, seal up bag, write date on, freeze. Then when you need to feed the milk you can defrost as many bags as you need to make a full bottle - it's common to get only a small amount when you pump so you need to combine output. FWIW though I was never pumping every hour.
- I don't know how to answer your last question, it just seems so hugely impractical, I would just feed the baby! It's not that much of a problem if you need to stop and grab a toddler. Most clothing which is breastfeeding friendly has kind of flaps, so if you did move suddenly, the flap would fall down and cover your boob anyway. Maybe I am just really laid back but I have never worried about feeding in public at all - it's never been an issue. I think it is one of those things that seems more daunting in your imagination than it is in reality.