1/. Properly do I understand the sentence? (<<< not correct) Do I understand the sentence properly? (<<< correct) 2/. No harm would have been done had he not noticed the key left in the door (is equivalent to>>> No harm would have been done IF HE HAD NOT NOTICED the key left in the door.) 3/.He not had noticed (<<< not correct) He had not noticed (<<< correct) Hope this helps! :) Good Luck :)

If the first question is in the past tense, which is most likely, it should be 'Did' rather than 'do'. Also, it would be more appropriate to use the word 'correctly' rather than 'properly', they have slightly different connotative meanings. 'Did I understand the sentence correctly?' is more appropriate than, 'Did I understand the sentence properly?'

Jerry, I am not. But I am trying to understand the rules of English.

I'm wondering if you're trying to impose Russian grammar rules onto English?