Yes, "it is common to be sleepy" and "it is common that one is sleepy" have essentially the same meaning. In this usage, "one" is an impersonal or generic pronoun that just means "any person". It tends to sound very formal, though.
"It is common that everybody can be sleepy" doesn't really make sense in English for a few reasons. "Everybody" is not the same as anybody or somebody: everybody essentially means "all people". You probably don't mean that all people are sleepy at once. If you mean "any person", anybody or anyone would be a better choice. Also, the word "can" is used to refer to possibility or ability, as in "I can run very fast" or "the baker can deliver the cake tomorrow". It doesn't really make sense to say it is common that everyone has the ability. When referring to a hypothetical, it's more common to use could or might, as in "Michael could be asleep by now" or "I might fall asleep soon". If you really want to use a phrase something like the third option, I would use something like "Anyone might be sleepy".