So why did Dirk kill himself and make Jake his his severed head in the synchronization? He woke up Jake so he didn't need to be revived via kiss. Did he need to die to wake up as his dreamself? why couldn't he have just gone to sleep?

His dreamself was knocked out, he needed Jake to kiss his head to wake him up so that he could rescue Roxy and Jane and travel back in time via teleporter in order to wake up Jake so he could kiss him.  It’s some paradox bullshit, but it was necessary.