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.
Best Answer
For the first part, I would be inclined to use "I am free" unless there's a specified point at which you will become free, e.g. "After lunch, I will be free for the rest of the day".
For the second, you certainly can use "today" instead of "the day". This is just preference, but "the day" sounds more natural unless you want to specify another day e.g. "I'm free the rest of today, or tomorrow morning".
"Yesterday" also works too, but sounds a bit clunky in your example. I think it sounds more natural without the "rest of" - so simply "After that, I was free yesterday".