Out-File -append in Powershell does not produce a new line and breaks string into characters

Out-File defaults to unicode encoding which is why you are seeing the behavior you are. Use -Encoding Ascii to change this behavior. In your case

Out-File -Encoding Ascii -append textfile.txt. 

Add-Content uses Ascii and also appends by default.

"This is a test" | Add-Content textfile.txt.

As for the lack of newline: You did not send a newline so it will not write one to file.