What to do if the mother is in Poland and her children, aged 17 and 14, in Ukraine but a neighbour could help them get to the border? Will children holding valid passports but having no visas and unaccompanied by their parents be allowed to cross the border?

The fact that children are under-age does not mean that they cannot cross the border. Just like in the case of adults, this depends on whether or not they are holders of a biometric passport (in which case there will be no additional issues related to them crossing the border) or a regular passport (in which case they need to submit an application for being recognised as refugees or apply for the Commander of the Polish Border Guard to allow them to cross the border). If a child crosses the border without either of their parents, they should hold a notarized permission to cross the border with a person looking after them. In practice, this document is not unconditionally required.