1. He saw his bird fly free.

2. He saw his bird fly freely.
(Which one should we use? Are both OK?)

3. They decided to call the baby Mark.
4. They decided to name the baby Mark.
(Are both the same in meaning?)

5. My vision is blurry these days.
6. My eyesight is blurry these days.
7. My eyes are blurry these days.
(What does 'vision' mean? Are they all the same in meaning?)

1 is the more common expression.

3 and 4 are both correct.

5 and 6 mean the same thing. 7 has to do with one's eyes themselves, not with what one sees.