Earlier today I installed the trial version of Gravity and I've added my personal twitter and facebook accounts.
I was pleasantly surprised by the G! icon on Sleeping Screen and when it changed to an envelope icon a few minutes ago I was impressed.
I checked the application and sure enough a facebook message had just been sent to me.
However, I can't find any way to open the message! Uh?!
The facebook bar/band shows my name with the envelope icon and '1' next to it. I tap on the fb bar and the fb new feed opens. I've searched and searched but I can't find an option to open the message.
After running Energy Profiler for fifteen minutes I found Gravity to be even more of a battery hogger than whatsapp, so I've uninstalled it. It averaged 109mA on a strong 3G connection while sitting idle in the background and the widget not installed on a homescreen. For comparison, my phone (N8 PR1.2) averages 6mA when idle and 9mA when Nokia IM Chat is in background.
In answer to your first question, I think you have to tap the Facebook account then swipe right to get to the messages.
As for the second, have you got the latest beta version from Jan Ole? http://mobileways.de/latest/gravity-beta.sisx/ (I think there was version sometime a go that drained the battery very quickly.)
Never tried profiling it but, although it seems to use more battery than Tweets60 that I was using previously, it doesn't bother me too much.