Your last message is still a bit fuzzy to me. At first it seems to have an inconsistency. You say that there was no '.aes' file found and then show a screencap with evidence that you have created five of them. Then re-reading your text, I <THINK> what you are saying is that those five files were created on a Windows PC, and now you are trying to decrypt them, and you are showing me five files you have copied from the PC, and telling me that you have dropped them on the icon, and that there is no unencrypted version around for any of them.
Correct me if this is not the case.
Now on to the second screencap ... and the really interesting part of this puzzle.
This is a bit strange. It appears that the program has successfully associated itself with the '.aes' extension, (otherwise the '.aes' files would not show a lock icon for them') but has failed to install, or I should say, be recognized. Right up front, I think your Mac is confused. I am not sure how to tell you to fix it, but the things you tell me point to the Mac being stuck in the twilight zone. Here is why I say this. You show a screenshot of a finder search showing that AESCrypt.app is not found ... and yet in your first message, you say that you dropped a file onto the lock and got a password prompt... So how can an application that isn't installed have a lock icon that triggers a password prompt??? I think your Mac has Alzheimer's. I have seen something similar to this before in my Mac a long time ago with some program I was trying to install. I ended up in Mac hell where I could not copy an application into the Applications directory because it was owned by root, and I am not root, and I could not install a new version because the old version was there and owned by root, and I couldn't overwrite it. Some secret magic inside the Mac is supposed to handle this for me. In much the same way it works on Windows 7, when a user tries to install something, it asks if you want to let the app make changes on your computer and then it secretly runs the install as Administrator. Mac does something similar and really performs the copy as root, except for some odd reason this was not happening on my Mac for this app. In the end, I dragged and dropped the old version of the app from 'Applications' in finder into the trash can. Which <DID> work, and magically cleaned up whatever was confusing Finder. Then I 'installed'.. (one of those 'Installs' which shows you an Icon of the App.. and arrow and and the 'Applications' Icon and tells you to drop the App icon on the Applications icon .. a silly install really because that is EXACTLY what it is doing!)
Anyway .. it worked this time. I wonder if we are into some similar exception to the 'it just works' rule.
Some questions for you:
* If you go into Finder and just click on 'Applications' under 'Places' is AESCrypt there? It should be.
* If you are dropping things on the lock, then it must be on the Dock somewhere. If you right click and select 'Show in Finder' where does it take you?
* You said you were able to run aescrypt from the command line, which means that you are familiar with using Terminal. Can you open terminal and cd into /Applications and do an 'ls' or 'ls -l' ... is there a folder named 'AESCrypt.app' there? (You can also use Finder and right click and select 'Show Package contents') If so and a search in Finder does not show it to you, then there is something broken in the Mac's view of its own world. I am no expert on the subject, but I don't think Mac really searches your whole drive when you do a search... it somehow keeps track of stuff you do and stores META information somewhere in some secret cache somewhere. If somehow something does not get written down, then finder gets confused.
* Anyway... if there is no AESCrypt.app in /Applications, then your install is messed up somehow. (I was going to make an install for this thing, and never got around to it.. sorry.. A Mac install does not do anything anyway but copy the '.app' directory into '/Applications'.) If there <IS> an AESCrypt.app then 'cd' into '/Applications/AESCrypt.app/Contents/MacOS' and run './aescrypt -h' .. this allows you to test the binary and see if it works. You can also test the encryption and decryption and see if the whole thing works.
* If it does not work. Then there is something incompatible between your system and the universal binary. If you have a compiler installed on your system, you can try downloading the source and read the instructions for compiling ... I think I just added '-l iconv' to the compile line to make the linking work. This should give you a functional binary. You could then replace the one in the Applications 'MacOS' directory (you may need to use 'sudo to do the copy.. not sure)
* if it <DOES> work, then AESCrypt is fine, and your Mac is confused. I would say to delete the installation, and start over. You should just be able to take the whole '.app' that you download and drag and drop it into 'Places->Applications' in finder.
* I think it is best to do this moving and copying in Finder. I think doing installs in terminal leaves the running system out of sync. It did not know you put something there, and does not update some secret cache somewhere. .. But this may just be voodoo superstition on my part. Generally my rule of thumb is ... do it in terminal if I <DON''T> want Mac to know I did it... and do it in Finder if I <DO> want Mac to know I did it.
Oh one last thing, which I have seen work on my Mac before when stuff like this happens ...(but don't tell Windows users because we make fun of them all the time for this) ... but ... did you try just rebooting your Mac?

I have seen cases before where something <DID> get written down properly .. where ever such things are kept .. but the running system did not notice... I did a reboot and suddenly a search for 'Aescrypt.app' in finder shows it right where we know it is ... in '/Applications' .. and everything works.