Your comments
Yes, you can upload any type of file.
If you want to know how to get pictures into Textastic from the Photos app, have a look at the comments in http://feedback.textasticapp.com/topic/9278-import-pictures-from-the-photos-app/ to see how you can do this with the Dropbox app.
How did you create the symlink? Do you have a jailbroken device?
If you have picture downloaded to your local file tree, you can tap-and-hold the file and select "Preview" to view the picture or tap on the button on the right side of each file in the file transfer screen and choose "Preview".
I use the official Dropbox iOS SDK: http://www.dropbox.com/developers/reference/sdk
It does use the REST API.
This if fixed for the next update.
Looks like a bug. As soon as you hide the keyboard, the behavior is back to normal for me.
See my answer below on when https is used.
Error -1004 is "Cannot Connect to Host". Please check your internet connection - the Dropbox server doesn't seem to be reachable.
Customer support service by UserEcho
I guess the second case is what happened in your case.