did you already started making the real game, or is this just the beginning of the project?
If you have just started, i recommend to not think about the animation of the explosion yet, first get your basic game idea ready, and then start adding new features like the animation.
for the arrowkeys, use the code bellow, with fighter

• as x-value and fighter[y] as y value of the spacefighter.

function on.arrowLeft()
     if fighter[x]>(min x-value here, eg. 0) then
          fighter[x] = fighter[x]-1
     end
     platform.window:invalidate()
end

function on.arrowRight()
     if fighter[x]<(max x-value here, eg. 300)
          fighter[x]=fighter[x]+1
     end
     platform.window:invalidate()
end


if you work with a platform.window:invalidate() called from a timer.start function, you don't have to put it there (if your period is small enough at least), otherwise you have to put it there to redraw the fighter on the new position.

and for the filesize, avoid using TI.images in the file, it makes it slower and larger. But if you'd like to use them to draw the spacefighter, you shouldn't hesitate, cause it's quite small.
i think you should first start programming everything you want, and clean it afterwards, otherwise you'll spend more time on thinking how to program something small instead of programming something good. once you know how it works, you can start cleaning it an certainly reduce the filesize

This is what I did for my blockbreaker : it handles a basic linear acceleration/deceleration (the "dx" part)
This allows the paddle (or whatever is moving) to have a smooth scrolling.

the paddleStuff function gets called when the ball(s) move(s) via a timer, from on.paint, basically)   

    ...

    function on.arrowKey(key)
        if key == "right" and paddle.x < platform.window:width()-20-XLimit then
            paddle.dx = 8
        elseif key == "left" and paddle.x >= 25 then
            paddle.dx = -8
        end
    end
    ...

    function paddleStuff(gc)
       if paddle.dx > 0 then
           paddle.x = paddle.x + paddle.dx
           paddle.dx = paddle.dx - 1 -- more if on-calc
       elseif paddle.dx < 0 then
           paddle.x = paddle.x + paddle.dx
           paddle.dx = paddle.dx + 1 -- more if on-calc
       end
    end


Hey, guys, I want to know something. I can't figure out how to draw things, so I found the smallest image of a spacefighter on google images that I could. I used ti-nspire scripting tools to convert it to a TI-Image. Nick, I tried using your script(The script you gave me is correct). But, when I defined the picture "spacefighter" as the TI-Image string, and then ran the script in nspire student software, the title screen shows, but after I press enter, the picture doesn't show. I didn't get an error message, so I obviously typed valid program syntaxes and arguments.

You should cross-post your questions in the Lua help sub-forum. You migth get some help faster there.