Crossword ability - still there!

I think I've got some justification in feeling a bit chuffed with myself. I've just completed a certain crossword in under 24 hours without resorting once to a dictionary, reference book or the internet (as well as having completed the 'Speedy Crossword' from the same paper).
    Doesn't sound very remarkable, but when I was between my late-teens and mid-20s I did manage, or attempted to finish, the 'Everyman' competition crossword from our Sunday 'Observer' newspaper every week, occasionally sending them off to try to win the prize - though it was never won by me. Then when I moved house and lived alone, away from my parents, the habit fell into desuetude. I'd always kept the resolution to resume this satisfying practice sometime, but it never transpired (through always thinking about lack of time) - at least until yesterday, some 40 years later!
The 'Everyman' crossword is by no means the most difficult around, though I don't think many would classify it as 'easy'. Clues are in the direction of being 'cryptic', though anagrams, letter sequences, abbreviations also all appear - and it helps to have a reasonable grounding of general knowledge.
   So, now that I know I still can do it, I'll probably make it a weekly feature. Flexing and using those brain 'muscles' and achieving the desired result is oh so very satisfying!

Now while on the subject, how about if I offer, purely for entertainment, three classic clues and publish the answers in a few days time? The first has become a bit of an old chestnut by now, but it's possible that some of you have not seen it before. It was posed to me by a friend all those decades ago. Even though I say myself that I did get the answer, eventually - that 'eventually' took some time to come.
The second I heard on the radio some years ago where the very clever answer was given immediately. I'm dead certain I would never have got it - but it's a word we've all heard and used.
And the third was one I did eventually get - but only after considerable research in the local public library. I should imagine that, using the web, it would be possible to come up with the answer in a very short time, perhaps even a few seconds.

Clue 1)    H I J K L M N O                 (5 letters)

Clue 2)   heggs                                   (11 letters)

Clue 3) What Methuselah and Madame de Pompadour had in common?         (12 letters)


So, if you're inclined have a go. None of them is impossibly difficult. Well after all, I got two of them!
If you work them out or want to offer an answer please don't write them in a comment (otherwise I might have to delete it) , though a comment that you'd got them, without giving away the answer(s) would be nice. But if you want to suggest anything to me by e-mail I will respond through that medium. However, I will be posting the answers here in a few days time anyway. Good luck!