Would it be less crowded if we booked to see the Gardens in the morning -- and the Palaces and Generalife in the afternoon when I have heard it is less crowded??

As I recall, Generalife IS the gardens; the palaces are in the fortress. One ticket gives entry to both fortress and gardens. There is timed entry to one palace complex (half-hour increments) but you are free to roam all other areas of the fortress and gardens before and after that specified half-hour.

The only timed entry is for the Palace. If you book a morning time (say 10am) you can enter the whole complex when it opens at 8:30 and see the gardens and the fort either before you see the Palace, after, or both if you want. It's just the palace that you have to enter during the half hour window on your ticket. I believe if you have an afternoon time you can't enter the grounds until 2pm. We had a 10am ticket, got there when it opened (at 8:30) and it was very uncrowded. We stayed till about 12:30. This was just a couple of weeks ago. Might be more crowded in the summer, but they limit the number of tickets they sell so I don't think it ever gets horribly crowded.

We also went again in the evening but I don't recommend it, I though it was not well lit and I was disappointed. But I loved it during the day.

I went during the day and then again that night, and enjoyed both visits for different reasons. During the day, you can see all open areas of the Alhambra. During the night, you can see only the Nazrid Palace. When I was there during the day, the Nazrid Palace was packed with people, and it was very loud. The crowds and sounds didn't prevent me from enjoying the experience, but it did make it hard to move around and to hear the audioguide. By contrast, there was almost no one else there during my night-time visit. It was so quiet that I could hear the water in the pools, and I could smell the delicate scents of the shrubs. Absolutely magical! It was one of the high points of my wonderful visit to Spain. Hope that helps!