1)
Was this the entire time from Yetzi'as Egypt?
1.
Radak: Yes. Every generation had sinners. In most generations, most were sinners, even though I constantly warned them via Nevi'im.
2.
Malbim: Yes - they did not go forwards once 1 , even though I rebuked them via all My Nevi'im.
1
This is difficult. They camped at Har Sinai 'like one man, with one heart!' (Rashi and Targum Yonasan, Shemos 19:2. I.e. their sole intent was to receive the Torah! - PF)
2)
What is "Yom Hashkem v'Shalo'ach"?
1.
Rashi: Every day, I was early to send [Nevi'im to fix them]. Radak - most warning was in the morning, before man goes to his work.