When is it appropriate to use the diminuitive form '+ek' (or +ka)?

My parents are native Polish speakers, but I have a bit of a hard time getting them to explain grammar to me (for them it is something they never really analyzed and thus takes a bit for them to explain to me). I'm thinking of saving the trouble and just asking you guys:
When is it/isn't it appropriate to use -ek?

If you want specific questions:
-Do you use it in formal speech/writing (eg a speech, an essay, a snobby gathering?)
-Can it imply cuteness?
-Can you add -ek (or -ka) to an animal to make it a term of endearment (well, not all animals)?
-Would you do it if you already have 'mały' (small) in the sentence?
-What are the differences (if any) between the masculine -ek, -ciek, -uń, -eńki?
-What are the differences (if any) between the feminine -ka, -cia, -unia, -enka, -lka?
-Any other things you might want to clarify about diminutive usage.
BTW for English speakers wondering what a diminutive is, it is close to how we have 'Tom' and 'Tommy', the +my indicates a child or a term of endearment.

-Do you use it in formal speech/writing (eg a speech, an essay, a snobby gathering?) - informal speech

-Can it imply cuteness? - yes (for example: "staruszek" - "staruszka" - 'old lady/man')

-Can you add -ek (or -ka) to an animal to make it a term of endearment (well, not all animals)? - yes (for example "kot" (cat) - "kotek" (kitten)

-Would you do it if you already have 'mały' (small) in the sentence? - no