Is it true after the first ejaculation, any consequitive ejaculation carries no sperm?

They're still there! The whole idea of ejaculation is to squirt sperm into a fertile woman and make a baby. Nature has made it so that if a man has sperm, they will be in each and every ejaculation, no matter where, when, or with whom it happens.
Wishful thinking. Sperm is present in the semen at all times, before, during & after the 1st, 2nd or 3rd ejaculation or more. It only takes one to trigger pregnancy. If you are having unprotected sex at any point other than the moment of ejaculation you will likely become pregnant.