(فَافْتَحْ بَيْنِي وَبَيْنَهُمْ فَتْحًا)
This means: Judge between us according to what each of us deserves, for "fath" (opening/judgment) here carries the meaning of adjudication. "Fathan" is a verbal noun (masdar); it is also permissible that it be an object in the sense of "maftuhan" (opened/adjudicated). This is a summary account of his supplication, peace be upon him, which is detailed in Surah Nuh.
(وَنَجِّنِي وَمَن مَّعِي مِنَ الْمُؤْمِنِينَ)
This means: Save me and those who are with me among the believers from their designs or from the calamity of their deeds. In this, there is an indication of the impending arrival of the punishment upon them.