I'd suggest you do NOT connect multiple characters in parallel.
The LEDs used in each character (7-9 of them) are in all probability matched to some extent and CAN be driven directly from the AA batteries without damage.
If you connect multiple characters in parallel the LEDs in the different characters may not be closely matched enough, and you'd see a large variation in brightness between the LEDs in each of the characters.
I'm not sure what tools you have to investigate, but we can surmise the likely operating characteristics knowing how the characters are powered.
If we assume that the characters use Alkaline batteries and the lifetime is only say 5 hours or so of continuous operation then from the Alkaline battery datasheet (Duracell MN1500 AA Alkaline) we see the following:
I assume that the LEDs are white, and these will have a Vf of around 3.2-3.3V at 10-20mA. A typical white LED would have Vf characteristics like this:
Since the highest voltage from the AA cell is about 3.3V, you can directly drive the LEDs without any series resistor. The current may start at close to 10mA but as the battery ages the cell voltage drops and so the LED current drops.
If you have 7-9 LEDs in each character then you can expect the battery current to be approximately 70-90mA for each character depending on the number of LEDs.
There are potentially several ways to implement a solution using a single power supply, but I'm going to suggest one way that may be a simple exercise for you.
From our favorite supplier search for a DC-DC converter based on the LM2596 with a digital voltmeter built in. They will look like this and cost somewhere in the $2-3 range:
Also source a 12V 2A power supply, the typical Walwart or block types. If you search for an LED 12V supply you will find what you need. While I've suggested a 12V supply, you could use almost anything over 9V (to keep the DC-DC converter happy). You may just have an old laptop power supply (typically in the 15-19V range) and even this would be more than adequate.
If you connect the power supply to the DC-DC converter your can turn the adjustment potentiate to get the required voltage to run the LEDs.
I've already said it would be bad practice to put all the characters LEDs in parallel so to fix this problem you need to put a series resister in place for EACH character.
For characters with 7 LEDs, I'd suggest a 1.5 Ohm 1/4W
For characters with 8 LEDs, I'd suggest a 1.2 Ohm 1/4W
For characters with 9 LEDs, I'd suggest two 2.2 Ohm 1/4W in parallel.
Your circuit would look approximately like this:
simulate this circuit – Schematic created using CircuitLab
Adjust the DC-DC converter to about 3.1V initially, the LEDs should all come on at least dimly. Slowly increase the voltage up to about 3.4V and the characters should all be reasonably bright and of equal brightness.
Since we don't know exactly the current flowing in the LEDs you may have to adjust the voltage to meet your needs, however you should not need to go above about 3.5V to get your required result.