What does "her features never set into a civil parade of attention" mean?

This is very fancy language! It is using internal puns and cross-metaphors to convey the meaning that the person in question is - or, at least, looks as if she is - paying attention to whatever is going on. A 'civil parade' (or any parade) is a formal procession, with everything in order and, very often, people standing to attention (as soldiers do). 'Civil', in that context, is used to mean 'not military' or 'civilian'. 'Civil' also means 'being polite', 'having good manners'. Both words come from the Latin 'civilis' meaning 'to do with the city' and, in one sense, therefore, meant 'people who are not in the army' but was also used to refer to people who were more cultured than country people. The writer is making a pun on the two meanings of the word 'civil' and also on the two meanings of 'attention' (people standing to attention in the manner of a formal parade and the act of being attentive to what someone is saying). By combining the two ideas, he is also implying that someone who looks as if they are paying attention may not actually be doing so!