Hi,
First, regarding the number of wake locks.
The device's battery usage stats in system settings is a more practical metric. I mean, holding a wake lock in the app -- or letting the system do it for you (as I suspect is the case for apps that plug into the system's account list) -- I don't really see a difference.
Second, Gmail push over IMAP is very expensive. IMAP push is expensive on its own, but with Gmail it's worse, because their IMAP IDLE implementation is incomplete (known since 2007, no plans to fix). The native Gmail app is very tightly integrated into the system, and use its own network protocol.
I wouldn't recommend having more than 1-2 folders in push mode for Gmail, maybe 3-4 if the stars align right (connectivity, the device's battery size, usage patterns, etc.)
Third, for the scheduled mail checks not working -- I could investigate if you recorded a debug log, capturing a few hours of the app's being in the background with the screen off.
Log instructions are here:
http://www.aqua-mail.com/?page_id=232Last but not least, if your WiFi system settings are to enable when the screen is on, disable when the screen is off -- consider trying AquaMail's built-in setting to establish WiFi connections for scheduled mail checks from sleep mode.
Just enable it in the app's settings (extended mode, under "Synchronization settings", labeled "WiFi in sleep mode", defaults to off).