T.T.
It's actually fairly typical for a child that age to suddenly become terrified of his bath. Try two things....fill the tub when he's busy doing something else, then bring him. The noise of the water might scare him a little. The other thing is drain the tub after he's gotten out and left the bathroom. Sometimes kids worry that if the water can go down the drain, they can too.
As far as the tantrums go, ignoring is the way to go, but first let him know that you hear him. Tell him, "I see that you're mad right now because Mommy turned off the TV. But I can't understand you when you scream and cry. Come and tell me when you're ready to do something with Mommy." Then walk away and let him have his tantrum. Validate his feelings, but refuse to listen to him when he's having a tantrum. Same things goes when he does get more vocal and starts whining. Make sure he knows that you'll listen to him when he's ready to talk to you in a nice voice. My daughter is also 16 months old so I know how it is!! Good luck, I'm sure you'll raise a wonderful boy.