Hi LuisB.
I’m not sure what to suggest about hiding the extensions. The reason you’re getting the error is that ‘extension hidden’ is a property of the file itself, not of the name. So you’d need to do something like this:
tell application "Finder"
-- Rest of code snipped snipped for brevity.
set new_file to (make new file at current_folder with properties {name:new_name, file type:"TEXT", creator type:"ttxt"})
set extension hidden of new_file to true
end tell
Or possibly:
tell application "Finder"
-- Rest of code snipped snipped for brevity.
make new file at current_folder with properties {name:new_name, file type:"TEXT", creator type:"ttxt", extension hidden:true}
end tell
The reason I’m not sure about it myself is that I always have “Show all filename extensions” checked in my Finder preferences. When I run the script with either of the above modifications, the “.txt” extensions are shown in the window anyway. They don’t get hidden. If I uncheck the preference and run the script again ” with or without the modifications ” the new files’ extensions are hidden but those of the originals remain visible. If I run the script again without the modifications and with “Show all filename extensions” checked, the extensions remain visible as expected. But if I then uncheck “Show all filename extensions”, only the extensions of the new files disappear. The extensions of the older files remain visible. 
With regard to creating the files and then writing text to them, there are a few combinations of approaches.
The simplest in your case would be to create the files as you have done and to use ‘write’ ” which is one of the File Read/Write commands, not a Finder command ” to write the text to each file as it’s created.
set ext to ".txt"
set some_text to "This is some very interesting text."
tell application "Finder"
set selectedFolder to selection
set current_folder to item 1 of selectedFolder
set theList to every file of current_folder
end tell
repeat with this_file in theList
tell application "Finder"
set cur_ext to name extension of this_file
set new_name to text 1 thru -((length of cur_ext) + 2) of (name of this_file as text) & ext
set new_file to (make new file at current_folder with properties {name:new_name, file type:"TEXT", creator type:"ttxt"}) as alias
--set extension hidden of new_file to true
end tell
write some_text to new_file
end repeat
Obviously the text used here is just for demonstration purposes. Also, ‘write’ has optional parameters which control the kind of text (Mac Roman, UTF-8, UTF-16) written to the file and whether the text is appended to the file or written over the existing contents.
Another approach would be to use the File Read/Write commands to create the files too. This is more complex and certain precautions have to be taken, but it can be faster if there are a great many files in the folder. I won’t confuse you with code for this here unless you think you may need it.
