If by "proper English" you mean "not offensive", yes they're proper English.
There are many other ways "pop into" is used. Other examples:
1. Pop [the pizza] into the microwave oven.
2. You should pop into the restaurant tomorrow.
There are probably much more. But I think the meanings are very close to each other so they will be easy to understand.
1. Is it a proper English adult and children should pick up? - 1. Is it proper English adult and children should pick up? No "a" because English is only one.