Is there a way to see aggregated stats for my empire?

Just hold the mouse over the research button and a window will pop up in the bottom right to show the number of military and civilian labs.

The only way I know of is when you exit a game, there is a screen that has a whole bunch of stats.  You can change the stat category with the buttons on the left of the screen, and see individual stats by clicking on the text in the lower part of the screen.  I can't remember if the ones you are looking for are in there, but that's the only place I know to look.

Ahh thanks, mbaron's info was exactly what I was looking for Thanks for your answer, too, sawakaki, I had noticed that stats screen, but after the game it doesn't help much anymore ;D

To check your place among the factions click on a empty spot on the map then hold the mouse over the 3 small windows  to the left of the unit window (the window that has a small picture of selected units) They will have a small "medal" icon with a number rank for empire, military, and economy. Hold the mouse over either and a window will pop up to the right with more ranked stats for things like fleet size or research. It doesn't give exact stats but it does let you know where your empire is at in relation to the other factions.

You can also see that by opening the diplomacy screen and clicking on yourself

And the easy answer goes to Annatar11.   Hey, I woke up at 3:00 a.m. today and I'm a little slow.

Early waking/morning is a valid excuse.