Hi.
1. Is it correct to put the word 'of' here? If not, should I consider the phrase 'his own' as sort of an adjective?
He brought with him the stuff that is (of?) his own.
2. Would you be able to tell me some reasons for the different preposition use for these? Should I take the uses as being idiomatic and shouldn't be too deeply troubled by them?
It will enable you to trust God
with every detail of your life.
He should trust God
for every detail of his life.