When I open a tin or tube of tomato paste and have some left over I freeze it in an ice cube tray. As you need a tablespoon or two in future you just pop a few out of the ice cube tray.
I have found if you chop celery into stalks, wash and dry it, and wrap it in tin foil and put it in the fridge it has amazing preservation powers and the celery stays crisp for ages. I mainly use it in cooking but I think if you like raw celery it would be fine.
To poach a single egg as a snack, I just put 1/3 to 1/2 cup of water in a cup, break the egg into it, put a saucer or side plate on top and microwave it for a minute. Then drain.
To cook frozen peas, put them in a cup - no extra water- put a plate on the cup and microwave for a few minutes until hot. Saves boiling them in a saucepan and so easy.
Read online reviews of any appliance product you are buying. I have the most basic bare bones plastic electric jug which cost almost nothing and had great reviews for reliability. It has just gone on and on. The chic red enamel one I had wanted had the most awful reviews about the enamel wearing really badly. Avoid "extra bits" like automatic ice makers and chilled water dispensers that are likely to break. We got rid of a electric door bell that was always breaking down and need an electrician and now people use the original brass knocker to bang on our door. It's been there since the 1920s and is still going strong.
I do keep a bag of raw chicken trimmings in the freezer and when I have enough I make my own stock. It doesn't matter if it's fatty bits because when the stock cools it forms a layer of fat on top which you can just lift off. I simmer the chicken with a carrot, onion and a stick of celery if I have it. I freeze that in small portions too. Taking into account the simmering on very low heat for two hours you want to make a big batch. I am not sure this saves money over buying ready made stock but at least I know exactly what is in it. (I'm not in the UK and I think our electricity is quite a bit cheaper - lots of other things are dearer.) I guess you could use a crockpot if you had one.
I bulk cook casseroles. Stale bread can be whizzed in food processor to make breadcrumbs and frozen in a box in the freezer. When needed scoop some out and let defrost - it doesn't set solid for me at least. I'd use it for crumbing chicken etc.
I use white vinegar as fabric softener for the washing machine for a few things. It is handy to have in a spray bottle to spray on sweaty underarms in clothes to get rid of any residual smell.
I am miserly with paper towels. I have a cupboard stocked with lots of cheap microfibre cloths. Lot of the time you can just use a microfibre cloth and biff it into the washing pile. I live in a country where most people use cold water in their washing machines. The clothes do get clean and it's probably better for them in terms of durability. I tend to handwash stuff that is dry clean only and I have only had one disaster -a red silk and cotton top that just bled dye. Not talking about tailored stuff of course.
Strip baths are awful. I remember them from my childhood. They do save hot water but they were grim.
Buy gender neutral children's clothes if you can if you want more than one child. It is easier to pass on a red or navy coat or back pack to a boy sibling for example than a pink one. (But hey if you're not concerned with meaningless social customs crack on with the boy in the pink coat.) Choose for durability - dark colours tend to look better for longer. Check shoes for wear and tear and get new heels and replacing the toe bit of the leather sole when they wear. Or go for durable rubber soles.
If you sew, consider buying one of those packs of small mini reels of different coloured thread. Thread is expensive but if you only want a small amount to hand stitch a hem or do a discreet darn they can be very handy. Obviously chose a pack with colours that sort of go with the colours of clothes you would wear. Consider one of those little battery powered devices that whir over bobbled fabric. It can give a garment a whole new lease of life when it is no longer covered in bobbles. I never had much luck with the handheld version at all. If a garment is wrecked and is for the rubbish, I save the buttons in case I need to replace buttons on something else. I have a button stash.