To concatenate files you use
cat file1 file2 file3 ...
To get a list of quoted filenames sorted by time, newest first, you use
ls -t
Putting it all together,
cat $(ls -t) > outputfile
You might want to give some arguments to ls (eg, *.html).
But if you have filenames with spaces in them, this will not work. My file.html will be assumed to be two filenames: My and file.html. You can make ls quote the filenames, and then use xargs, who understands the quoting, to pass the arguments to cat.
ls -tQ | xargs cat
As for your second question, filtering out parts of files isn't difficult, but it depends on what exactly you want to strip out. What are the “redundant headers”?