1. I'm sick and tired of hearing you crying!
I'm sick and tired of hearing you cry!
2. I've got a rash on my face.
'Rash' is usually singular - it refers to the condition itself.
You can never use 'figure' to mean 'face' in English. This is a false friend between French and English.
3. In half an hour we're going to serve the soup.
This is fine.
4. Dry your hands off after washing them.
This is OK but the 'off' is unnecessary. It's more normal to say just 'dry your hands.'
5. Wipe your mouth because you've got lots of chocolate around it.
'Lots' is a suggestion to replace 'plenty'. Remember that 'plenty of' is not a translation of 'plein de..' - this is another false friend. 'Plenty' means 'sufficient', and it is positive - for example, 'We've got plenty of chocolate in the cupboard, so we don't need to buy any more.'
I hope that helps.