I killed all the bosses on the island, but because of the server lags I did not count these killings, I killed all the bosses, but the main boss I can not kill, because I already killed him, and without him I can not open the gate. What should I do?

I'm a little confused. It gave you credit for killing the bosses but no credit towards opening the gate? If so, you might want to reach out to the devs and let them know about that. That's a pretty groundbreaking bug.

He killed the bosses in the online mode but because of these horrible issues with the servers/connections, they lost the credit for the boss kills. It has happened to numerous players. This is one of THE buggiest launches of a multiplayer based game I've played in quite a while.

Ok my bad, I didn't understand fully. To the OP: Be patient, I would expect a patch very soon, if I'm right about things.

i cant seem to figure out how you get out of the first area like where you spawn after the start

The devs said on twitter that an update/patch will be released today (Friday)