It’s the first prize I’ve won in sports.

[diamondcutter]

1. It’s the first prize I’ve won in sports.
2. It’s the first birthday I’ve spent far away from home.
(Made by me.)
Do I use the present perfect tense correctly in these two sentences?

 

[Barque]

Have Do I used the present perfect tense correctly in these two sentences?

Yes.

In the second sentence, note that "away from home" and "far away from home" don't mean exactly the same thing. Please consider if you need "far" or not.