Children and their families fleeing Ukraine can stay in Romania for 90 days without a visa. You don't have to worry about being forced to return home after this time. You are not required to present travel documents when crossing the border if you are trying to escape the armed conflict in Ukraine, but you may be required to present a personal identity card, so don't forget to bring the most important documents with you: internal passport, foreign passport, birth certificates.
To travel without a visa to the countries of the European Union that have agreed to allow this - the Schengen area - you will need a biometric passport - passports that have a chip that can be scanned electronically. Biometric passports have an icon on the front that looks like a sign with a dot in the middle. In many countries, you will need to register via the national authorities, UNHCR, or local authorities for assistance. For more information regarding the registration procedures in Romania, see the UNHCR Romania website.