Both are correct. It's just a matter of British vs. American English. American English tends to drop the "s."
Preference. I personally add the "s" at the end because the "s" sound just makes things flow more by slurring the words together a bit for me. Consistence is key.
I've been actually wondering about this a long time, whether it's a matter of AmE vs. BrE or just completely random. Guess the important thing is to stick to one, don't mix them up. I use 'afterwards' and 'towards.'