Why not: "they are waiting for the fourth child"? What suggests here that it is about expecting a child?
Čekají čtvrté dítě. = 'They are expecting their fourth child.'
Čekají na čtvrté dítě. = 'They are waiting for the fourth child.' čekat na + acc = 'to wait for sth/sb'
Ceska veta nerika nic o tom jestli cekaji "jejich" dite... proto nevidim duvod proc do anglicke davat "their"
Yes, you could, but it wouldn't sound very natural. "Své/svoje" would be better than "jejich." Nevertheless, it sounds the best if omitted.