"Thanks, how are you?"
Yes, it should be. Did you get marked down for it? If so, please report it so that we can go over it.
"Teşekkürler" is a plural form, meaning 'thanks' in English. "Teşekkür ederim" is like 'Thank you', cause "Ederim" is a verb that means: 'I do' + "Teşekkür"(can be a noun singular: thank).
Nasılsın is singular and informal. Nasılsınız is plural, formal or both.
I tried "mersi" for "thank you" and it counted it as wrong. Is it correct or am I wrong? Additionally, the given answer was "sağ ol". I've never seen that phrase. What's the difference between sağ ol and other forms of thanks?
"sağol" is another casual way to say "Thanks", it is informal. If you want to be more formal, there's another phrase you should use, which is "çok teşekkür ederim", it means "Thank you so much".
"Mersi" is not a Turkish word, it is a Romanian phrase which means "Thank you". That's why it was counted as wrong when you tried it because it's not a Turkish word.
I saw a website that mentioned it as a Romanian word once, maybe they wrote it wrong. it's so similar to "Merci" in French.
In case you didn't know, Duolingo actually offers you the Turkish letters which you can't find in your regular keyboard, it's underneath the blank space where you write your answer.