I like games on words, so even if English is not my mother tongue here are my answers :
1. Rearrange the letters of the word eat to make something to drink. tea
2. Rearrange brush to make a kind of bush. shrub
3. Rearrange lemon to make something else to eat. melon
4. Rearrange skate to make a poet. Keats
5. Rearrange wand to make a time of day. dawn
6. Rearrange Alice to make another woman's name. Celia ?
7. Rearrange Dorothea to make another woman's name. Theodora
8. Rearrange supersonic to get part of an orchestra. percussion
9. Rearrange hormone to get the name of a bird. (A little tough.) ??
10. Rearrange spectrum to make some eatables. crumpets
11. Which food might you make out of stale lamb? ??
12. What do you have to be if you want to listen? silent
13. Which word describes lithe acts? athletics
14. Which part of a newspaper may be an adroit lie? editorial
15. Which animal would you not touch with a bargepole? (Tough! Think of a kind of shark with a dog breed in its name) ?? (I was thinking about "beagle" for the dog breed ...)
16. In two words, where can you find a schoolmaster? ??
17. In two words, what is worn by a stripteaser? ??
18. Which London regions or suburbs are anagrams of canto, Hamlet, leaches, and poems? (For the Londoners out there) Soho, ??
19. Rearrange stealer to make a Shakespearean character. Laertes
20. Which part of the body is a ten-letter word in which the last five letters are an anagram of the first five letters? (located on the inside) intestines
21. Make two other words from the letters of idolatry. ??
22. Make three other words from the letters of the word gallery. ??
23. Make four other words from the letters of the word players. ??
24. Make four other words from the letters of inlets. silent, listen, ?, ?
25. Make four other words from the letters of the word maneless. salesmen, nameless, ?, ?
26. What quality might characterize a prime dunce? ??
27. Which adjective might describe a problem in Chinese? ??
28. In three words, what characterizes the nudist colony? ??
29. Which gambling event may seem like totally inane rot - especially if you lose? national lottery
30. Which German opera asserts the fact that a kinder love's rare? ??