"They are studying, like us."
Translation:Αυτοί μελετούν, όπως και εμείς.
It should be σαν εμάς, but I don't think it works here because of the different case. If it were the object, then yes (e.g. Αυτοί δεν είναι σαν εμάς - They are not like us). Also, it's frequently said as σαν κι εμάς. Here it's more like Αυτοί δε μελετούν όπως (μετελάμε) εμείς.
Υes you could. Not sure if it's used that often in english though. For example, maybe in that case you'd prefer to make it specific, like "They study/are studying Psychology, like we do/are." or "They study/are studying at Harvard, like we do/are" ^.^
Μελετώ and διαβάζω for study are safe enough, though ^.^ I hope I helped.
Since the Greek says "μελετούν" I think it refers to learning the lesson not attending a school etc.
μελετούν, όπως και εμείς marked as mistake. do you really need αυτοί in this sentence?
It's fine, this exact sentence had simply not been included, added now.