The bonuses are a huge 25% for each production type per government upgrade
This was an old rule for government upgrades. Now, each form of government appears to only add a cumulative 10% to your economy (so +10% for republic, +20% for democracy, +30% for federation), although I think there is also a hidden morale bonus. All you ever need is to keep morale at 60% and you will win all of your votes.
jwburks, I would try and figure out a way to drop your trade income and just leave the UP. What percentage of your income does it really represent? Also, when you have to declare war, you can still just attack another enemy ship to declare war. What will happen is you attack the ship, and a dialogue will pop up telling you that this is an act of war, but you can't attack till next turn. So your ships don't fight on the turn you declare, but you can still declare without going to the diplomacy screen.
On my 3rd day in this particular game... is this normal?
It really depends on the size of the map you play on. It also sounds like you are still learning the game. I have played (way too) many galciv2 games - but I also don't have a lot of free time thanks to work, and women just don't... understand spending lots of time on this game. With practice, I find it takes me 2-4 hours per map size, so 2-4 hours to play through a tiny map, 4-8 hours to play through a small, 6-12 hours to play through a medium, etc. The range is because map sizes are also effected by the number of habitable worlds, number of opponents, research rate, etc.
Sounds like you can win any way you like with a healthy tech advantage. Good luck on your first vicotry.