Here are the answers to your questions:
The faster I write, the more mistakes I do. (a) the
It was nice of you to take me to the airport. (a) to take
It's the worst meal I've ever had. (b) the worst
We saw that the train went slowly. (c) slowly
Susan is an engineer. She's also a mother. (b) also
London is the biggest city in Britain. (d) the biggest
I was very sorry to hear that news. (d) to hear
Have you ever been to England? (a) ever
This is a weekly newspaper. (a) weekly
Julia doesn't understand this rule yet. (c) yet
My desk was moved by someone 5 minutes ago. (c) was moved
When shall we finish all this work? (d) shall
She's getting a new job, isn't she? (a) isn't she
She will reach the Jamaican coast at 4 a.m. (a) will reach
Who designed St. Paul's? (b) designed
Have you found the keys you lost? (b) Have
Don't do that! Jane asked to them. (c) asked
Before she began her university course, Jane had read all the books on her first year reading list. (a) began, had read
Last week I was at a conference in York. (c) was
The weather has improved. (b) has
Who met you at the airport? (d) met
It has been raining for two hours. (c) has been raining
Every time when I missed the bus, I had to return home late. (b) had
When you grow older, you'll change your mind about this. (b) grow
"Come home on Christmas Day, we'll be waiting for you," my mother always says to me. (with on being the implied answer)
If you have any more questions or need further assistance, feel free to ask!