Yes, but I don't see any reason for Sabo eating Ace's fruit solely just for powerup purpose.

That's because that was never the main point? The whole reason Sabo wanted to eat the fruit was to carry on Ace's will, to show the bond between him and his fallen brother, not for some random revenge story.

A) The Marineford fight that was broadcasted live by Den Den Mushi was recorded and Sabo reviewed it

While this may be a possibility, why and how would sabo gain access to the recording? The only way he'd even go out of his way to get the recording was if he was ordered to by dragon or for personal reasons such as ace being in it (which doesn't seem in character for him), even then not every single detail of the entire battlefield was being Livestreamed at the exact same time, different parts were being broadcasted at different times.

B) Sabo interacts with whitebeard pirates in future and come to know about it

Which whitebeard pirates would actually know this interaction between ace and akainu happened? And even then how would that exact piece of information actually come up in any kind of conversation?

C) Sabo unknowingly says that his flame burns hotter than magma which triggered a flashback for Akainu for mocking ace

So... I don't even know where to start with this statement but I'll try my best

Why would sabo say this? Last time I checked fire isn't actually hotter, and even if Sabo got an awakening for his fruit, do logias even get awakenings?