This is a two part question.
Firstly, I would like to ask which of the following two sentences is the correct construction.
- I am free for the rest of the day
- I will be free for the rest of the day
Personally, I believe it's more logical to say "will be" as it's not in the present. Then again, number one is also quite common.
For the second part of my question, I would like to know if I can replace "the day" with another word like "today" or "yesterday":
- I will be free for the rest of today.
- After that, I was free the rest of yesterday.
Logically, there doesn't seem to be a problem with either, but since English is very much based on usage and rules, I can't confidently use them without some opinions/answers from native speakers.