Here are my corrections, I hope they help:

1. I'm not going to feed you, you're a big boy/girl now and you can feed yourself.

2. Eat up (name of the child), it's getting late.

3. We're not going to watch cartoons now, we'll watch the cartoons later after you've had a sleep.

4. When you finish your dinner, you can have some sweets/dessert.

5. Please don't shout, I can understand you much better when you speak quietly.

All the best

Emma (Talk2Me English)

1. I won't feed, you're already big. You have to eat yourself.

I'm not going to feed you, you're big enough to feed yourself.
2. Do not be distracted, eat faster.

You're getting distracted...hurry up and finish eating!

Don't get distracted... hurry up and finish eating!
3. Now cartoons not going to look. Look after sleep.

You can't watch cartoons now, you can watch them after you(r) nap.
4. You first need to make dinner, and then we have the sweet.

You need to eat your dinner before you can have sweets/dessert.
5. Don't shout! Speak softly.

Shhhh, don't shout/yell! Speak softly/quietly.