Thank you Semphyra for the inputs.
The SCL-CUZ flight is a good idea. However it doesn't operate on my date of travel and I need to travel on that day. So I still need to transit in Lima.
For my questions number 3, I have just found out they have changed my CUZ-LIM flight in the other booking as well. I should be able to change it to a preferred timing.
I'm surprised that LATAM hasn't notified me any of these changes. I found out all these by myself after checking my flights in their app... They normally don't send any emails about schedule changes?