1) Lucy about it. (to speak) 2) The students 3) Look! There are so many biscuits! Mark and Alice (to bake) the test since eight o'clock. (to write all morning. 4) He 5) The builders a house recently. (to buy) twenty houses since last year. (to build) here? (you, to wait) 6) How long 7) Ugh! Jack 8) It's Mary's birthday tomorrow. She my private messages! (to go through) her birthday party for weeks. (to plan) 9) They 10) Emma the walls in the nursery. (to paint) her hair red. (to dye) the dishes and hasn't done anything else since morning. (only. 11) He to wash) 12) Who 13) Wow. The flat is spotless! The kids 14) The artist my sweets? (to eat) all morning. (to clean) 15) These people the painting. (to finish) here since 2001. (to live)

Here are the sentences with the verbs correctly conjugated:

1. Lucy is speaking about it. (to speak)
2. The students have been writing the test since eight o'clock. (to write)
3. Look! There are so many biscuits! Mark and Alice have been baking all morning. (to bake)
4. He has bought a house recently. (to buy)
5. The builders have built twenty houses since last year. (to build)
6. How long have you been waiting here? (you, to wait)
7. Ugh! Jack has gone through my private messages! (to go through)
8. It's Mary's birthday tomorrow. She has been planning her birthday party for weeks. (to plan)
9. They have only washed the dishes and haven't done anything else since morning. (to wash)
10. Emma has dyed her hair red. (to dye)
11. Who has eaten my sweets? (to eat)
12. Wow. The flat is spotless! The kids have been cleaning all morning. (to clean)
13. The artist has finished the painting. (to finish)
14. These people have been living here since 2001. (to live)

Feel free to ask if you need more help!