This should fix your original issue. However im not sure how changing the graphics for BG1/2/3 would make you fall through the world. A video or some screenshots would greatly help.
So assuming that you already followed the steps to enable the "bitmap to map16" feature, use super gfx bypass (

) and replace AN2 with an unused ExGFX tileset.
Find a large open space in your map16 editor and select/hover over the tile you want your image to start at.
In the statusbar of the map16 window you should see a hex value for that tile. For example mine was D00. Keep this number in mind for later.
Now you're going to want to paste your image into map16 (Ctrl+V). After doing so you should change the colors that the image will use. You should probably copy the settings and what i do in this gif.
Now click the other options button and copy these settings, replace the circled region with your number from earlier followed by the blank map16 tile you want your image to stretch too. Just add 100 to your number and you should be fine.
Click "OK" and there shouldn't be any errors. If there are any the image you chose is probably too large.
Next you can save in your map16 window and place the image in the level.
After all of this be sure to export and import your ExGFX files.
(Press

then

)