"This is a good plan." --- "Yes, I hope to make it happen." "live" would sound strange.

"This is a good plan" "Yes, I hope I can make it live" is good, but better is ... Can use the phrase "make it live" in such a context?: "This is a good plan" "Yes, I hope I can make it go/work. 'work' is the usual word.

A good way to express this - especially in a professional context would be to talk about 'delivery.' "This is a good plan." "Yes, now we need to deliver it (or deliver ""on"" it)"

In this case, as said above "to make it work" would fit better. However, you can say "to make it live" in other contexts but it would sound as obligation or something forced. Kind regards.

This is more a matter of style in a particular culture. In my country, it would be more appropriate to say: 'I hope I can bring it to fruition', 'I hope I can follow through with it', or 'I hope I can execute it'.