Okay, I think I could help you. I picked up Diddy Kong a month or-so ago as an "others" character, since I really like the feel of playing him and he is still a quite popular tournament pick, so there is plenty of footage of top players using him, of course. I am a Mario and Duck Hunt main, but Diddy is still one of my better characters, so I could give you a few tips.
First of all, the short-hop, F-air, fast-fall is something to practice. It is one of the fundamentals of Diddy's mobility and tech. To practice it, go around doing it over and over again until its muscle memory. There is also a slow way of doing it (which isn't the better way). If you try to fast-fall instantly during the F-air animation thinking that that way you would fast-fall most quickly, you will actually be fast-falling slower than possible. Instead, just wait, and when Diddy fully flings his feet out in front of him, and maybe even then some, fast-fall, and you will find yourself doing these way faster. Also, make sure to F-air as you jump, not as you fall, because that would be less optimal and would give you landing lag. In certain situations, you can do it that way, but that would be just to hit people too far down, this not applying to his main technique (if that makes any sense whatsoever).
Another set of things to learn are Diddy's advanced techs. The Peanut Popgun B-Reverse Cancel can be a very useful tool. When side-B-ing (the harder you flick the control stick, the farther you will fly), hold the shield button until you do the B-reversal, which would normally have Diddy either charge the popgun or fire it, killing your momentum, but here, it will automatically cancel, keeping the momentum. You can also reverse down-B without holding shield in the same situations for mix-ups.
The banana is another of Diddy's tools, and yes, it is important to hold on to it for a little while sometimes. If you then see an opening, you can get a free grab/running up-smash/down-tilt into running up-smash or grab, or really anything. You can also glide-toss the banana (like almost any other item that can be grabbed), which is when you cancel your jump while tossing the item in any direction and getting a short slide instead. Just run and then press the jump button at the same time as you throw the banana. This is muscle memory for me, so I do it every time I toss the banana while running. Utilize this tool to its fullest.
Well, that was a mouth-full. There is definitely more, but those are the fundamentals of playing Diddy Kong. Also, watch ZeRo, MVD, Jtails, and other top Diddy players so that you could know how playing Diddy should look.
Hope that all of this helps!
Also, some links to useful videos -
Glide toss tutorial:
https://www.youtube.com/watch?v=G3_vOtY5kCc
ZeRo's Diddy plays at EVO 2015 (some of my favorite of his):
https://www.youtube.com/watch?v=JrxZaPGlMh4
Jtails Diddy guide:
https://www.youtube.com/watch?v=FytxBGjH17I
Jtails Diddy For Glory:
https://www.youtube.com/watch?v=eQKZiE2VUD0 (You can see some of the things I talked about here, plus more that I didn't mention.)
