Is karde and shode used for 'has done' and 'has become'?
Also do you need to have ast after these words (in informal writing and conversation)? Can I please have examples of when کرده and شده are used?

For example 'the car has become dirty' is 'mashin kasif shode'.

mersi

Question

Is karde and shode used for 'has done' and 'has become'?
Also do you need to have ast after these words (in informal writing and conversation)? Can I please have examples of when کرده and شده are used?

For example 'the car has become dirty' is 'mashin kasif shode'.

mersi

Answer

Yes you can omit it in informal speaking....

Answer

The verb 'Shodan" in Farsi means 'to become' but you should know that it is an auxiliary verb with which you can turn an active verb into the passive one. ie. I broke the window من پنجره را شکستم ------The window was broken = پنجره شکسته شد. 
we need 'ast' after 'Shode' and 'Kardeh' in formal writing or speaking not in conversational just in third-person singular forms.