Play it safe and bring the items & copies. Embassy certifies your passport and translation services along with the MFA (Minister of Foreign Affairs) certifies the translation. Not too hard but not speaking from personal experience (no babies in Thailand that I know of)
No problem but you can return on visa exempt (no visa) dont need to apply again for a tourist visa, (with USA passport) you get 45 days. May be asked to show a ticket leaving within those 45. Once you leave Thailand, your original visa is history.