Dear native speakers of English, please check my dialogues [There is no plural] with my son. Thanks.  (We are Russian speakers.)

I've put written down some of our conversation. dialogues [Too formal here, since we now know it is between you and your son] I am just wondering if we are speaking conversing with each other correctly in English.  (some foreigners do We make mistakes but we don't realize we do so, it for they sounds ok for to us! :)

Our dialogues conversation/chat/talk

Mom, can I watch a cartoons?
Finish your meal first and then you may can watch a cartoon. [This is understood. When we speak, we prefer to use short sentences and to the point]
Mom! The cartoon has ended. is finished, Can I watch another one?
No, Sorry dear. [This sounds harsh] Enough of cartoons for today.

Where's is [too formal for a chikd] daddy? When is Daddy he coming home?
Daddy's at work. He'll coming [To formal speaking to a child] be back in the evening.

Daddy's home!
Hi, Dad! I missed you so much.
So did I. Look what I've got for you (taking out a toy from his bag)
Wow! Can I see it?
Dad! I love itIt's great! [I assume your child is small] Can I play with it now? Yes, sure! Go ahead! [You really need to have those exclamation marks to show enthusiasm; otherwise the father is sounding rather non-charlant.

OR

(taking out some candy)
Can I have one?
No, sorry, you can't. [This is mean!.  If he didn't want to give don't show and torture the son!] Sure but only after dinner.

Ok.
When can I have it?
You can have it after dinner.

Dad, I've finished my [too formal in the conversation] dinner's done!, Can I have a candy it now?
Yes, Sure! Go ahead.
Dad, Can I want have more  [Shows that you have not taught your son polite manners]
Ok. Here you go
(The little brother tries to take snatch the candy from the big brother)
Hey! It's mine!! Don't touch this!

Writing dialog is as difficult as writing prose.  It must convey the mood, the emotion, the feelings and the cultural/age/background/context of the speakers.  This is called scriptwriting.  You can win an Academy Award for this.  It is a highly specialized form of writing.