FFVI: Divergent Paths

I'm really new into the FFVI modding, basically I use the tools the community created (mainly ff3usme) and watched some video tutorials by B-run.

Used the search a lot on this forum and learned a lot. About the code this is a little new to me, but I want to try to fix this issues. You recommend to try to change with a hex editor?

I take it the tutorial by B-Run was about changing field sprites?  If you used a hex editor to place a change like that, you might have put it at the wrong spot.
Also, of the programs available to edit FF6SNES, make sure you DON'T use ZoneDoctor.  It's fine as a resource but it has a disastrous save bug that ruins the ROM.

What I recommend is this:

(1) Take Lunar IPS and make a difference patch between Divergent Paths 1.1 and your altered Rom.  DP should be the original [unmodified] ROM you pick for the file selector, and your changed ROM should be the one you pick when the program asks for the modified file.
(2) While Lunar IPS is still open, click on the check box that says "Create a Log File".  This will generate a list of rom addresses that are changed by a patch, every time you use a patch.
(3) Make a copy of your ROM and apply the patch you just made.  This shouldn't change the file at all because the IPS patch only contains values that are different between DP 1.1 and your changed file.  Keep this copy, we'll be doing hex editing in it later.
(4) Open the text file that was generated as a log of this patching.  Look for addresses that are six digits long and start with 2E [That's the $EE bank].  They will be listed as an address and a length of difference, so you might see something like 2E7786, 14.  That means that 0x14 bytes were changed by the IPS file.
(5) Open both your modified file and Divergent Paths 1.1 in a hex editor [I use HxD personally].
(6) Use the search function to go to the addresses you saw in the text file, the six digit ones starting with 2E.  Do so in both files.  Copy the number of bytes from the DP 1.1 file into your modified file that matches what the IPS log states.  Hopefully the amounts will be short, but you should be able to just safely copy a bunch of bytes anyway because we're trying to repair ROM damage.  In fact, you could hypothetically select the block $2E0000 to $2EFFFF in DP 1.1 and paste it on your modified copy [Paste write, not paste insert, starting at $2E0000].
(7) Load your save file and see if the falcon is still broken.  Check for other graphics that might have been reverted to Vanilla by this change.