Translation:I lost my wallet at the store.
You could use "wasureru" in a similar circumstance to this question. However, "nakusu" means "to lose something" and "wasureru" means "to forget something" or as you pointed out "to leave something carelessly behind", so even if the meaning is similar, it's not the same. If the English says "lost", then I think it should be "nakushimashita".
If you know it's in the store... then i would argue that it is not lost - it is left carelessly behind. Lost implies (to me) that it is missing, but you do not know where where it is. The English sentence only works if you are physically in the store, and you think you lost your wallet in that store, but not sure where exactly.
Yep, wallets and purses both exist here, men use wallets, I'm sure some men use purses but you don't see it often here, women seem 50 50 split on wallet or purse usage, sometimes they use a wallet but refer to it as a purse to make things complicated, I've never asked my friend why she does that, but I'm assuming the answer is that she regards purse to be the femenine word for wallet.
My preference though is big ol' coin buckets. Can't live without 'em.
Japanese children's books do the same with the spacing, it does make reading easier (because I've also had to read the occasional children's book with no spaces, and that never goes well). When there's no spacing, you have to do your best to identify the particles, which helps divide the words.