Indirect speech: can you tell me if this is ok?
(the words I wrote are written in capital letters, please check the tenses)

She asked me what MY NAME WAS, then how old I WAS.
She asked me if I HAD a driving license and what foreign languages I COULD SPEAK. She also asked me about my present job- she asked where I WORK at present and how much I EARN there.
She asked me which school I WENT to and when I HAD FINISHED school. She asked me what I HAD STUDIED since I left school and finally she asked if I HAD questions for her.

Question

Indirect speech: can you tell me if this is ok?
(the words I wrote are written in capital letters, please check the tenses)

She asked me what MY NAME WAS, then how old I WAS.
She asked me if I HAD a driving license and what foreign languages I COULD SPEAK. She also asked me about my present job- she asked where I WORK at present and how much I EARN there.
She asked me which school I WENT to and when I HAD FINISHED school. She asked me what I HAD STUDIED since I left school and finally she asked if I HAD questions for her.

Answer

MY NAME WAS - my name is
I WAS - I am
I HAD - I have
I COULD SPEAK - I can speak
I WORK - I work
I EARN - I earn
I WENT - I went
I HAD FINISHED - I finished 
I HAD STUDIED - I have studied 
HAD - have

There are several ways these sentences could be written with the same meaning, however I have only changed the words in capital letters to make it sound more fluent.
I hope this is helpful.
Julia

Answer

That is all spot on. Only slight thing is in the final bit people would say '...had ANY questions...'

Answer

Yes, it all looks OK.

Despite what some grammar books tell you, there aren't any hard and fast rules regarding when to 'back-shift' the verb tense in reported speech. We generally use our common sense about what sounds best, and your answers sound fine.

Cute kitty, by the way.