Anagram Dictionary

This puzzle is taken from a Martin Gardner book I read years ago. It’s a favourite of mine.

I want you to imagine a dictionary. Not an ordinary one, but one geared for anagrams. Each entry is an alphabetical list of letters, with any words using those letters listed afterwards. Some entries are straightforward. ANV, for example, would just have VAN as its word. Others would have a 2 or 3: AEELPS would list ASLEEP, PLEASE and ELAPSE.
Around half the entries would be under A. This is because so many words contain this letter. Whilst many shorter words do not, there are far more longer words that do.

I have a few questions for you to ponder.

1. A would be the first entry (with the definite article A listed as its word) and AA would be listed as the second (a type of lava). What might the third entry be?
2. What would the first entry under B be?
3. BIT, ALLOY and LORRY are all entries, yet words in themselves – that is, the letters are in alphabetical order. What is the longest such entry you can think of?
4. AEGINLRT would list several words – 5, I think. Can you find them all?
5. What is the longest entry that wouldn’t repeat any letters?
6. Difficult one now: what might the last entry in the dictionary be? Be careful with this one!

I’ll post some hints in a couple of weeks, and the answers in a month. Until then, happy puzzling!