Morale in GalCiv isn't like in many other games. If your morale is above 50%-54% your population will grow, which will cause morale to drop. So a civilization at equilibrium will have -all- planets at 50%-54% morale or so, that's normal. What morale-boosting social projects like the Multimedia Center really do is increase that planet's max potential population (they increase morale by a set amount, at which point your population on that planet grows until morale once again drops down to 50%-54%).
As far as money problems go:
1. Make sure you only build social improvements that are worth the upkeep cost. My first five projects are soil enrichment, habitat improvement, banking, research lab, and then manufacturing center. The first three of those have 0 upkeep, the last two cost 1 each, that's a lot of empowerment for just 2 upkeep.
2. Make sure you only settle planets that are of a quality of 15 or higher (planets with a lower quality than 15 actually cost money to support instead of making it).
3. Initially set your tax rate to 50%. This is too high for the long-term, but when you first start all your planets have such low population that you can run your taxes this high and still have 100% morale on each planet. Keep an eye on your planet list (F2), later in the game when you notice morale dropping on all your systems start lowering the tax rate by 5% at a time till eventually you get it down to 35%. I'm not positive that 35% is the best value, but I've found it works for me and the AI's like that value as well (they usually are at 38% or so). Don't keep lowering taxes past that point just for morale, as I noted above morale will -always- eventually drop to 50%-54%, thats perfectly normal.
4. Don't build too many starbases. The upkeep on them is 5 each, you can seriously hamper your economy if you have a lot of starbases. Make sure when you build a starbase that it will be worth the upkeep.
5. Trade tech for money with the AIs. I usually pick 2-3 techs, then go to each AI (don't forget the minor AIs) I have contact with and sell them at XX credits for YY turns. I try to set XX low enough that YY is between 10 and 20 turns. You can make huge amounts of money this way (the better your diplomacy rating is versus theirs the more you'll make, try to make sure that you get the trade good Diplomatic Translators), which allows you to pump up your Expenditures slider for YY turns (thus increasing your ability to build ships, social projects, and research tech).
6. Don't go overboard on espionage. When I first meet an AI I set the espionage up 1 click from 0, that's all I've found to be needed. Later in the game when you get the message that your espionage against a given AI is at the Advanced stage set the slider back down to 0, I've found no benefit from continued investment beyond that point.
7. All the above will give you a sound economy, but if you want even more strength in that area then you can choose custom picks before you start the game that boost economy. The Federalist party gives +20% economy, and you can also boost economy with one of the custom picks. You can choose a morale boost as well, which translates to an economic bonus because what a morale boost -really- does is increase max planet population (which, combined with planet quality, is what determines the economic output of a given planet). My last few games I've been using a custom set composed of the Federalist part combined with +30% economy, +10% morale, and +30% research. That's a 50% boost to economy total (plus the extra you get later with the extra population the 10% morale boost gives) combined with 30% research bonus, I'm very fond of this initial setup for any size galaxy.