Well, "zaraz" is difficult. It's not exactly 'right now', but 'almost now' :D 'in a moment' still seems the best to me. For example if my mother asks me to wash the dishes and I'll say "zaraz!" to her, I will come to the kitchen 5 minutes later. So it's open to 'interpretations' as well.
Anyway, the continuous 'will be reading a book' sounds strange to me with 'right away'...
In English there is no such concept like aspect but it is present in Polish. What helps to distinguish perfective from imperfective in English are tenses.
Imperfective verbs don't have in Polish separate future form but the future tense is compound of future form of the verb "być" + past form of the imperfective verb or infitive. Look at the table of conjugation: https://en.wiktionary.org/wiki/czyta%C4%87