We will arrive in Barcelona in the afternoon, a day before our tour starts. Is there enough time to visit Monserrat before we meet up as a group? Also, when we go to Granada, will there be opportunities to visit Alhambra during the day as well as at night? Any suggestions of things to do during our free time?
According to the description, the tour begins at 5 pm. Montserrat will not take a full day. The question is whether you'll be up to it the day after arrival. I guess it depends on whether you want to hike there or just see the monastery. It sounds like the tour takes you to the Alhambra in the morning and you have the afternoon free to stay there or do something else. I'm not sure what the qualification "when available" means. If there is a night tour of the Nasrid Palaces or the Generalife that night, you could go back for it. Sunset's at 9 pm so it would be a very late night for you.
The Alhambra is included in the tour and will take an entire long morning. The tour includes dinner on the hilltop facing the Alhambra, with a famous night-time view of the place. (I'd have to say I liked the view better than the food at the particular restaurant my group used.)
Granada's cathedral and the royal chapel next door are well worth seeing on your free time. The RS guidebook has a self-guided walking tour of central Granada that is kind of hard to follow but includes some good sights.
EDIT -- Are you asking about use of free time throughout the tour or just in Granada?