I know that using “a” and “the” correctly is a big problem for many Japanese. But wouldn’t that have been a good reason to have a native speaker check this sign?
“Currency exchange machine” is countable. There is only one in this bank. The sign is not referring to something that the reader already knew about, so it’s correct to use “a” here, rather than “the”.
“Mail” and “insurance” are generally uncountable nouns, so it’s strange to see them as plural forms on these signs.
“Savings” sounds natural, but not because it’s a plural form! “Savings” means the amount of money that you currently have saved. We can refer to a bank account that’s intended strictly for saving money as a “savings account”.