Explanations

1st joke

DON'T BOTHER= don't worry, I'll do it (you don't need to take the trouble).
In colloquial British English (or black American English), "I'll ask her" sounds the same as "Alaska".

2nd joke

KAYAK= An Inuit or Eskimo boat made of wood. You can see the picture of modern kayayks here: Kayak.
CHILLY= Cold.
CRAFT= A ship, a boat or an aircraft (airplane).
SANK= Past tense of the verb to sink (to disappear under water): sink-sank-sank
ONE AND FOR ALL= Definitively.
It is a play on words that sound alike: You cant have your Kayak-cake and Heat-eat it too. The word KAYAK is pronounced /kaɪæk/, and if you say it quickly it sounds a bit similar to CAKE /keɪk/. And the word HEAT /hi:t/ sounds similar to EAT /i:t/.

This is a rather bad joke, but it's good to remember an English proverb: You can't have your cake and eat it too, which means that when given a choice between 2 mutually exclusive desirable things, you can't have them both. For instance, you can either eat a cake, or you can keep it for later, but you can't do both. Unless you only eat part of the cake, but that doesn't count.. ;)
If you want to marry a nice lady and explain to her that you love her, but you need to go out with other girls too, she may tell you: I'm sorry, but you can't have your cake and eat it (that means: go to hell you idiot, and don't phone me again )