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Introduction to logic

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I need help on Quantifier logic problems?
Using the symbolization key given, symbolize each sentence in QL.

Universal Discourse: animals
Dx: x is a puppy
Hx: x is lost
Tx: is a Terrier
Fxy: x can run faster than y
r: Tim

1.No puppy can run faster than Tim.
2. No animal is faster than itself
3. Some puppies are Terriers and some are not.
4. There is a puppy who is not a Terrier but is faster than any Terrier
5. For every puppy, there is some animal that is faster.

Here is my attempt:I'm uncertain about question 1 and 4 and I need more clarification on those.
1. ~∀x(Dx --> Frx)
2. ~∃xFxx
3. ∃x[(Dx & Tx) & (Dx & ~Tx)]
4. ∃x[(Dx & ~Tx) & ∀yFxy]
5. x(Dx--> ∃yFxy)

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