I think I might have some answers to a lot of the issues going on here.
(Just based on what I've seen so far)
Freeza being revived in pieces
Because it would be cool/funny. Toriyama/Editors probably have some kind of gag to go along with him being in pieces, or just simply think it'd be cool and/or more "recognizable" for him to be in pieces. Think about it; which image is more popular when it comes to Trunks defeating Freeza? The one where his chopped chunks are floating in space next to trunks, or the one where the burning embers are falling to earth? You probably won't find an "In Universe" explanation because there probably isn't one. It's simply storytelling aesthetic.
Freeza coming back at all, and stronger at that
As said above, this isn't the first time we've gotten "New and improved" villains. His latent power 4 months of training, on top of the whole "death" pun, is just a reason they came up with to give him leverage in a fight against the current strength of the cast. He's got that much power hidden within, he can bring it out in only 4 months of training. That's it. It is what it is.
Clearly, the self proclaimed prodigy and genius who ran an entire planet trading organisation didn't stop to consider that maybe he should train to make sure that he could beat the man who almost killed him. No this was something that had to happen twice before he had the common sense to think training might be a good idea.
So basically he's just an idiot then.
No, he didn't. Because, as you (and Goku) has said, he's a fool. An arrogant fool who's so prideful and sure of himself that he probably talked himself into thinking his defeat at the hands of Goku was a farce. And then lost to Trunks because he, with his new Cyborg fittings, once again overestimated his strength.
Hell's Angels
"Haha wook at the adorwable things and mean ol Freezer face"
You got it. That's probably it. Besides promoting Clover Z, they're only purpose is to be a funny contrast to Freeza. A gag.
"Oh hey they're doing something meaningful...only not since there is no struggle to handle mooks are all so weak anyone beyond Roshi could wave their hand and kill them all".
Except, knowing Dragon Ball, they'll probably end up being really strong despite their looks (another popular "gag" in the series) and wipe the floor with Freeza...or maybe they can't be killed. This is all assuming they even fight at all.
I'm not saying these holes or questionable things aren't there, and there are things I'm a bit "eh?" about, too ( Freeza only "recognizing" the Dragonballs as "mysterious orbs"?) but...like EX said, just chill. Be laid back, be super shounen!
And he has Zenkai, that's why when he got back from his destruction, he became stronger. Does Freeza have Zenkai?
