Mon père coupe l’ananas, et ma mère prépare une salade de kiwis avec quelques prunes.

Because French possessive adjectives agree with the thing possessed, not with the owner.

• mon = my before a masculine singular noun
• ma = my before a feminine singular noun

So:

• père is masculine → mon père
• mère is feminine → ma mère

Both mean my, but the form changes to match the noun.

French normally shortens le or la before a word starting with a vowel or silent h. This is called elision.

So:

• le ananas → l’ananas

This makes pronunciation smoother.
Also, ananas is masculine, so the full form would be le ananas, but in real French you say l’ananas.

They are in the present tense.

• coupe comes from couper = to cut
• prépare comes from préparer = to prepare

Because the subjects are Mon père and ma mère, both verbs are in the third person singular form:

• mon père coupe = my father cuts / is cutting
• ma mère prépare = my mother prepares / is preparing

It can mean either one, depending on context.

In French, the simple present often covers both:

• My father cuts the pineapple
• My father is cutting the pineapple

and

• My mother prepares a kiwi salad
• My mother is preparing a kiwi salad

French usually does not need a separate form like English is cutting unless the speaker wants to emphasize that the action is happening right now.

Because de is commonly used to show what something is made of or what kind of thing it is.

So une salade de kiwis means:

• a salad made with kiwis
• a kiwi salad

If you said des kiwis, that would usually mean some kiwis as a standalone noun phrase, not the normal way to describe the type of salad here.

So:

• une salade de kiwis = natural
• une salade des kiwis = would sound like the salad of the kiwis, which is not the intended meaning

avec means with, so it adds another ingredient.

• une salade de kiwis = a kiwi salad
• avec quelques prunes = with some plums

This tells you the salad is mainly presented as a kiwi salad, and the plums are extra ingredients included in it.

Because quelques already functions as a determiner, meaning some or a few.

In French, you do not normally stack des in front of quelques.

So:

• quelques prunes = some / a few plums
• des quelques prunes = incorrect in this sentence

This is similar to English: we say some plums, not the some plums.

They are plural because the sentence refers to more than one kiwi and more than one plum.

French usually forms the plural by adding -s:

• kiwi → kiwis
• prune → prunes

In writing, that -s marks the plural. In pronunciation, though, the final -s is usually silent.

Usually:

• père: the final -e is not pronounced as a separate sound
• mère: same idea
• kiwis: the final -s is normally silent
• prunes: the final -s is normally silent

So the plural is often visible in writing more than audible in speech.

The comma is possible here, but it is not strictly necessary.

French often does not use a comma before et, just like English often does not before and. But a writer may add one to separate two clauses more clearly:

• Mon père coupe l’ananas et ma mère prépare une salade...
• Mon père coupe l’ananas, et ma mère prépare une salade...

Both are understandable. The comma mainly affects rhythm and clarity.

A rough English guide:

• l’ananas sounds approximately like la-na-na
• quelques sounds approximately like kelk

A couple of useful notes:

• In l’ananas, the l’ links directly to the next word.
• In quelques, the ending is compact, and the s is not pronounced.

French pronunciation is smoother and more connected than English spelling may suggest.

Because French normally uses a possessive adjective directly with family nouns when saying my father, my mother, and so on.

So you say:

• mon père
• ma mère

not:

• le mon père
• la ma mère

French does not combine a definite article with a possessive adjective in this kind of structure.