Translate into predicate form. No one hates Bob. [H = “is hate”] ∼∃x∀y H_b
Translate into predicate form. Dogs are not reptiles. [D = “is a dog”, R = “is a reptile”] ∀x(Dx⟶ ∼Rx)
Translate into predicate form. Nothing is blue. [B = “is blue”] ∼∃xBx or ∀x∼Bx
Translate into predicate form. [C = “is cat”, M = “Mars”, A = “mammals”] No cat lives on Mars. Unless all cats are mammals, Bob, the cat, lives on Mars. Therefore, only mammals are cats. ∀x(Cx⟶∼M), ∀x(∼Cx⟶Ax) ⟶(C B ⟶Mx) ⊢ Mx⟶∃xCx
What I need help is are these the correct predicate translations for these sentences so I need some feedback if they are translated correctly.
You quantify an $x$ and a $y$ ... but don't use them in the actual formulae that is being quantified. So, the quantifiers end up doing nothing.
Also, what are the $x$ and $y$ supposed to be? The $x$ could be the person (not) doing the hating of Bob .. but who or what is $y$? .... The $y$ is unnecessary.
So ... what we need to say is 'there is not a $x$ such that $x$ hates Bob'
This translates as $\neg \exists x \ Hxb$
Good. You correctly surmised that this English statement is most likely meant to be about all dogs.
Also good! Note that likewise for number 4. you could have done $\forall x \ \neg Hxb$
First premise is: $\forall x (Cx \to \neg Mx)$ (you forgot the $x$ in $Mx$). But we can also ranslate this as $\neg \exists x (Cx \land Mx)$ ('there is no cat that lives on Mars')
Second premise: "Unless [P], [Q]$ translates to: 'If not [P}, then [Q]
Now, your [P] here is: all cats are mammals, which is $\forall x (Cx \to Ax)$
While the [Q] is: 'Bob is a cat and lives on Mars', which is $Cb \land Mb$
Putting these together, we thus get as the translation for premise 2:
$\neg \forall x (Cx \to Ax) \to (Cb \land Mb)$
Conclusion: 'only mammals are cats' This can be understood as: 'For anything: if it is a cat, then is is a mammal'. And so this translates as: $\forall x (Cx \to Ax)$.