As MMM said か can be used to translate "or". However this particle it is used to link 2 nouns. I think what you want to know is about linking phrases. Unfortunately at the moment I can think only to a couple of example and yes I would write them as 2 separate phrases. If you write down what you got in mind, maybe it reminds me of something different
As per 時 you can translate is "when", it usually help to get less confused.
MMM gave you the kanji of 時間(じかん), which if you get to understand those 2 kanji will make you understand easy the difference.
時=time
間=interval of time.
The role of the second kanji can be more easily understood when you face the hours. 一時 shows "the time when it is 1" so basically 1 o'clock. 一時間 shows an interval of time which lasts 1 hour. Just to help you coz I usually I confuse people when I try to explain something, I give you an example.
一時（いちじ）に食（た）べた。 Ate at 1 o'clock.
一時間（いちじかん）食（た）べている。 Have been eating for 1 hour.