They do verify immediately in many places. The cash register scans the check, extracts the bank routing and account numbers, and does an EFT transaction on the spot.
Yeah. Then they hand the paper check back to you. (I haven't written a check, or seen anyone write a check, at a store in many years, but that's how it was working the last time I did see it.)
Depends on where you are for "paying extra". Grocery stores in the US around me don't charge differently for credit/debit/check/cash. Restaurants are starting to charge credit card fees to people but have a cash/debit "discount" which I'm actively ensuring I use. Probably going to hit up the card companies and explain that the change in cost means their cards are worth less now and I'll just never use them.
I have two hands. One is occupied by my wallet that I just took the cash out of. The other is occupied by the change that was just handed back to me. Which hand am I supposed to push the cart or carry my stuff with? Just be patient for a moment.
You could put your wallet away while the cashier is putting your cash in the drawer and getting your change out. However, if you're at one of the longer lines that has the conveyor belt it's unlikely you'd be holding up anyone behind you because they're not likely to be ready to check out in the short period of time it would take to put your change away, and it's not like putting your change away is going to stop the cashier from starting to scan the next person's items.
I put my wallet away, grab my stuff with one hand, then take the change with the other hand & stuff it into a pocket. Then I sort my stuff when I get in my car.
I like to inconvenience myself so that strangers who don't care about me can save 2 seconds in the lineup. Then I go around telling people what a great guy I am for it.
And that's not even with a kid. Try pushing a trolley, holding a kid, and putting your change away.
I tried an palm scanner recently at the grocery but felt like OP as I scanned it several times and it never was able to recognize my palm as a palm.
Nah, I'll do it right when the cashier hands it back to me at the check stand before I grab all of my stuff and then walk out so I'm not fumbling shit all over the walkway and impeding even more people. 10 seconds isn't going to kill you.