The way I'd be inclined to handle this is as if it were a program which ships with a corpus of clip-art, then selects and arranges elements of that corpus according to user-provided instructions, expressed via an input string.
Firstly, it is well-established here that the licence on a piece of software does not generally affect the licence status of the software's output. So in answer to your first question, the licence status of the generated image is, most likely, a function of the licence on the letter shapes.
We have several questions around here already (eg this one, and this one) which advance the idea that the code and the other digital assets in a piece of shipping software do not have to be under the same licence. If you distribute your code under AGPLv3 and the letter shapes under (say) CC BY 4.0, I think you will achieve the desired effect: people offering your code to others, including as a network service, will have to provide full AGPLv3 source, whereas anyone using the output images need only credit you.
For maximum compliance, it may help if your program makes it clear when it produces the output that, as a consequence of the use of inputs supplied by you, the output is under CC BY. Also, when split-licensing like this, it is very helpful not to mix the two bodies of differently-licensed content. If the images can be loaded from an external file, rather than being incorporated into the program, it helps avoid misunderstandings about which licence covers any particular element of the distributed whole.