Present Progressive Passive vs. Infinitive Passive

Is this sentence correct?

A letter is being written.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

She is hoping to being elected president.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

My car is be fixed. I’ll order a taxi to get to work.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

The carpet needs to be washed.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

These doors should be shut at night.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

These doors should be shut at night.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

This window may be opening but that one must stay closed.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

Exercise are being done by them.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

Alice could be given a prize for her artwork.

• Yes, it is.

• No, it isn't.

Is this sentence correct?

I am expecting to be given a pay-rise next month.

• Yes, it is.

• No, it isn't.