I was born in Bristol, have lived in Bristol, Teesside, the west coast of Scotland, Pennsylvania, Texas, Teeside again, Chester and London. I live in London now.
1. A body of water, smaller than a river, contained within relatively narrow banks?
A rivulet, or an irrigation channel. Depending.
2. What the thing you push around the grocery store/supermarket?
A shopping trolley.
3. A metal container to carry a meal in?
A foil takeaway dish
4. The thing that you cook bacon and eggs in?
A frying pan
5. The piece of furniture that seats three people?
A sofa
6. The device on the outside of the house that carries rain off the roof?
A gutter
7. The covered area outside a house where people sit in the evening?
Veranda.
8. Carbonated, sweetened, non-alcoholic beverages?
Fizzy drinks
9. A flat, round breakfast food served with syrup?
Pancake
10. A long sandwich designed to be a whole meal in itself?
a baguette (you want sub or hoagie, in which case I'm hoagie fer sure).
11. The piece of clothing worn by men at the beach?
knotted hankie
12. Shoes worn for sports?
Trainers
13. Putting a room in order?
Tidying up
14. A flying insect that glows in the dark?
Firefly
15. The little insect arthropod that curls up into a ball?
? Hedgehog?
16. The children's playground equipment where one kid sits on one side and goes up while the other sits on the other side and goes down?
See-saw
17. How do you eat your pizza?
With a knife and fork, crust first.
18. What's it called when private citizens put up signs and sell their used stuff?
Huh. Car boot sale, but they drive it somewhere first. Or a garage sale but we don't have those here.
19. What's the evening meal?
Dinner.
20. The thing under a house where the furnace and perhaps a rec room are?
Cellar.
bohemiancoast
biascut's additions:
21. That plant that kids throw at each other because it sticks to clothing?
Goose grass
22. Those little balls of froth on plants in spring, which contain some moth or other's eggs?
Cuckoo spit
23. Girls' lower-half underwear?
Knickers
24. Boys' lower-half underwear?
Briefs
24. The cloth you had when you were little and always slept with, and perhaps sucked your tongue with?
Pussycat. OK, it wasn't a cloth.
yonmei's additions:
25. Warm knitted top typically made of wool?
Jumper
26. Baked in an oven, made of flour, butter, an egg, milk: raised with a chemical baking powder (cream of tartar/bicarbonate of soda) rather than with a yeasty leaven: what do you call it?
Well, there are several of these. Yorkshire pudding.
27. A single thistledown seed flying free? no idea.
? Hedgehog?
Wow, hedgehogs are insects where you are. That really is a regional difference. Here they are birds with giant teeth that gobble you up if you don't look under the bed at night.