That is or That was or both correct?

Hi. Please help. I am sure the parts in parentheses is optional, and for no. 3, I think we can either look at it as to mean to say "that is" or "that was." Also, could we have the phrase "that was" in the number 2 sentence? Thank you in advance.

1. He was excited because today was his birthday. He looked at the present (that was) given by his father. He then proceeded to open it.

2. He is excited because today is his birthday. He looks at the present (that is or that was - both correct?) given by this father. He then proceeds to open it.

3. I found out something new about him today. He still uses the golf club (that is or that was - both correct?) passed down from his father. It was a surprising bit of fact.