Across

10. Remember that an anagram may involve single letters indicated by longer words or phrases.

11. Don't ignore the word “on.”

12. Here, for once, the word “in” doesn't mean something will go inside something else.

20. Don't assume this refers to clue number 12.

22. Don't ignore the word “to” — it makes up part of the answer!

26. If you're not at home, what are you?

30. How's your knowledge of computing? The answer here isn't talked about on its own much these days, but more often as the second part of other words.

32. There is a very short word that means “to exist.”

Down

1. Think of Roman numerals.

13. This one's just a double definition.

14. Nothing to do with clue number 4.

15. This one does refer to the answer at clue number 4!

28. What sorts of window can you think of?

29. This one is another double definition.