Yes there was a condition, that being repentance. Otherwise, Hezekiah would not have had his life extended by 15 years.
No there absolutely was not. But feel free to point where it was in the exact word spoken:
"Thus says the Lord: Set your house in order, for you shall die, you shall not recover."
There are certainly instances where we're told the Lord changed his mind. Usually for the good of those who plead for mercy.
Now, is someone going to suggest that: (1) The Lord determined the Trump would be inaugurated on Jan 20, 2021, (2) told his prophets to spread the word, then (3) changed his mind?