What should one do who missed prayer while traveling until returning home; should he pray it in shortened or full form, and what is the interpretation of the noble verse: "If you avoid the major sins which you are forbidden, We will remove from you your lesser sins and admit you to a noble entrance"?

If someone forgot a prayer while traveling, or prayed it without ablution, and then remembered this after returning, they must pray it fully without shortening it.

As for the verse: (If you avoid the great sins which you are forbidden to do, We will expiate from you your [small] sins and admit you to a Noble Entrance [Paradise]) [An-Nisa:31], its meaning is that Allah expiates minor sins by avoiding major sins and performing acts of obedience.

Scholars have differed on the definition and number of major sins. Some said: every sin that Allah concluded with fire, wrath, curse, or torment. And some said: every sin for which Allah prescribed a legal punishment (hadd) or a threat. It has been established in the hadiths that some major sins include associating partners with Allah (shirk (definition)), killing a soul, sorcery, consuming usury, consuming the property of an orphan, turning away on the day of battle, slandering chaste women, disobeying parents, and giving false testimony. Avoiding these major sins expiates the evil deeds (minor sins).