The answer to both of your questions is: both of them die. This is because Deathtouch "works" during a fight, while First Strike does not. I realize this is a little counter-intuitive, but the way First Strike actually works is to create an additional damage step in the combat phase. Since the fight mechanic isn't the same thing as your combat phase, First Strike never triggers.
Think of it this way - Fight just makes both creatures do damage to each other. Period.
1) Prey Upon is played, naming Typhoid Rats and Primeval Titan. Do they both die, or just the rats?
2) Prey Upon is played, naming Typhoid Rats and Village Ironsmith. Do they both die, or just the rats?
Thank you very much.
Think of it this way - Fight just makes both creatures do damage to each other. Period.
If your answer is "No," then your morality does not come from God's commandments.
If your answer is "Yes," then please, please reconsider.