You could omit it but I think it would imply that 'they are studying in the same way as we are', not just stating the fact that they are studying and we are studying too. Here και is necessary in order to bring that 'as well' quality to the phrase.
Τι νόημα έχουν οι ερωτήσεις στα ελληνικά, που πρέπει να γράφουμε στα ελληνικά αυτό που ακούμε. σίγουρα δεν έχω καταλάβει κάτι???
Another odd underline: https://screenshots.firefox.com/EMQajYyQRMqTnEXr/www.duolingo.com . Why ´ing´? ´Study´ is also correct. I prefer my translation because it preserves the subject form εμείς rather than ´us´, but I know the vernacular ´like us´ would be a common usage.
Ok, it's a matter of word order. We have among other sentences of course: "They study as do we." this is rather an old style and a bit stilted.
We'll add your more up to date sentence.
"They study as we do."
Why Duo underlined the "ing" brings us back to the odd issue with the sentence we discussed yesterday. I'm reporting it again. Thank you for the screenshot.
Almost, you need the accusative case for that to happen. "Σαν εμάς" ;)
While it essentially means the same, the "so+verb to be+personal pronoun" structure has its own translation in Greek. Examples:
-Dude, I'm so tired (=Φίλε, είμαι τόσο κουρασμένος)
-So am I. (=Το ίδιο και εγώ) (Literally:The same and I)
-We're going abroad next month (=Θα πάμε (στο) εξωτερικό τον επόμενο μήνα)
-Nice! So are we! (=Ωραία! Το ίδιο και εμείς!) (Literally:The same and we)