Billie's mum bought Blue from his guitar teacher when he was 10, not his dad. The Blue that you see on stage currently is the original one. He has used replicas during other tours but that's while still using the original as he normally has a back up in case a string breaks mid performance while using it.
In the late 90's his replicas were blue Stratocasters that had different stickers but he eventually gave them away/stopped using them. Then in 2005 his backup was just a sunburst Stratocaster (you can see it in a few live videos). Starting from the 21CB Tour he started using a Fender Telecaster as the back up, the ones he would also give away to fans, and he kept using these up until the Trilogy tour. The only exception is during the South American tour for 21CB, Blue needed some repairs so he got another (darker) blue Stratocaster with different stickers and used that, that hasn't been used since though. Starting from the RevRad Tour he had a Buddy Holly replica Strat with stickers that he used as a back up but after he gave that away he started using a green Stratocaster called Swamp Thing which I don't think he used but now he has a custom Les Paul Junior called Blue Junior.
Blue has had many different repairs over the years but nothing too major. It still has a lot of it's original parts (you can tell by the look of them) but he has definitely changed the tuning pegs, the pick up, and most likely the wiring. I imagine the biggest repair he's had to it is a neck press so the neck stays straight/how he wants it.
So to answer your question, yes him mum gave him Blue, yes he still uses it, yes he's had replicas, and no it's not on it's last legs.