what you mean by “twitter icons”? Are you using Firefox?
Sounds like a file association issue. Try right clicking one of the files and opening it with firefox.
If you don’t already use it, try running this to see if your have some malware from Twitter or somewhere else:
I know this does not help after the fact but a thumbdrive only cost a few dollars. stick it in the usb port every once in awhile and save your files.
also a good rule to follow is this. use 2 computers 1 that goes on the internet at 1 that never does. keep important work in the offline computer. if you need to get something from internet use of thumb drive and then scan it first. if the online computer gets something inside it you can just wipe out the hard drive and start over