For your last post, Cell can improve. If he stayed the same he wouldn't be able to keep up. However, he could get on Beerus' radar and surpass SSB Goku if he trained for four months. IPC was incomplete, so it's no surprise that his KHH wasn't up to par.
DNA is a set of molecules that has the entire make up for an organism. Only 2% of that base is used for unique coding. Cell is given that 2% base to be uniquely coded to be better than Freeza. That tiny fraction includes everything good about Freeza, including his ability to make ridiculous gains in a short period of time. When you say "part of his DNA" that makes no sense and seems to just be a layman's interpretation of what DNA means. He's given the best unique qualities sure. But it's not like you do less well because you've only taken the best parts. Freeza's training ability would be part of "best parts", and the coding transfer wouldn't lose any number of months needed for training or anything like that. In fact, a good scientist like Gero would be able to reduce the number of months by observing the DNA pattern that Freeza has and improve on it. There's a reason Gero believed Cell was a perfect being over Freeza.
Outside of just DNA you can just apply common sense. Would PC only get a partial Zenkai? Obviously not. Cell unlocked SSJ2 from a single Zenkai. It took years for the person with the most potential to do that.