Please use the good words, GE means Graphic Engine, it's not a processor.
Everything Graphic related is always done by the GPU (Graphics Processing Unit, that's probably your confusion here)
- What is a texture:
It's just a "file" (let's keep it simple) who contains lots of image (or just one actually, doesn't matter) by Texture mapping it means they'll know where they belong.
For instance now it's easy to do a mario game and you could just need one texture for the whole background.
This is a texture:
- What is the format of PSP textures"
whatever the programmer wanted it to be, even if there's some "classic" format but it's not really PSP related.
- I tried replacing some printing characters, which are encoded in SHIFT-JIS, with ASCII and it doesn't show up. I tried stepping through in GE debugger.
That has nothing to do with graphics. It's comprehension related. You can take your own example backwards btw, you're trying to force English into something Japanese. Where does it says that Japanese cares about English ? Do they really need their games to have support for ASCII if they don't need it ?
Same goes for you, why would you use only ASCII and not the whole shift-jis encoding ? (ok there's UTF but I'm just explaining here)
If you want a concrete example, half of the text of Sword Art Online: Infinity Moment does NOT support Ascii at all. The japanese uses UTF8 and UTF16 as encoding (my guess is that there were multiple teams and they didn't bother to get the same encoding)
So what I did is simple, I've fucked UTF16 so it'll only accept single byte characters no matter what. Because it was: A=0x0041, not A=0x41 so AB = 0x00410042 (useless heh ? Try that one btw, it might work out for you)
And I'm a bit tired to answer everything so I'll leave at that right now