A few questions about Toei Broly

[Fantastische Hure]

1) Why was Broly so power-ful? He was born with a battle-power of 10,000. Was this Toei really trying to make it seem like Broly was destined to be the next "legendary" SSJ from birth or was that a mutation? If the former, does that mean Broly and the previous SSJ are related?

2) Why did Broly save Paragus as a baby? He clearly went insane later-on?

3) Did his power make him go insane? His power was huge and he never really trained for it, it just came to him, is that what made him go crazy? Like power over-load.

4) Was Broly becoming an LSSJ in movie 8 the first time he ever became that? In the flash-backs we see that Broly was already out-of control when he was a child/teenager, yet we only see him as an SSJ, how come? Did he acquire LSSJ for the first time, right when he's about the fight Goku? In that case, why does Paragus seem to act so nonchalant about that? If he hasn't seen that before it'd be surprising.

5) What's with the fate/destiny stuff about Goku & Broly?

6) How happy was Takao Koyama when Broly really turned-out to be higher than Bills, just like he'd like to have thought before?

 

[Pocket-Gog~]

You should refer to him as the OG Broly.

 

[Fantastische Hure]

"old gai" broly?

he wasn't that old

 

[Captain Cadaver]

1) Why was Broly so power-ful? He was born with a battle-power of 10,000. Was this Toei really trying to make it seem like Broly was destined to be the next "legendary" SSJ from birth or was that a mutation? If the former, does that mean Broly and the previous SSJ are related?

Both, probably; the former for narrative purposes in hyping him up and the latter as more of an in-universe rationale.

2) Why did Broly save Paragus as a baby? He clearly went insane later-on?

"Later on" after years of having his power/true nature restrained by his father who then was willing to abandon him to die on New Planet Vegeta. Meanwhile, he was the only sort of attachment infant Broly had and was directly in the vicinity to him.

3) Did his power make him go insane? His power was huge and he never really trained for it, it just came to him, is that what made him go crazy? Like power over-load.

It would be one reason, though Paragus restraining that power for years surely didn't help.

4) Was Broly becoming an LSSJ in movie 8 the first time he ever became that? In the flash-backs we see that Broly was already out-of control when he was a child/teenager, yet we only see him as an SSJ, how come? Did he acquire LSSJ for the first time, right when he's about the fight Goku? In that case, why does Paragus seem to act so nonchalant about that? If he hasn't seen that before it'd be surprising.

Most likely for reasons you already mentioned. LSSJ was something likely brought on specifically by Goku's presence fuelling his rage.
Paragus' reaction (or lack thereof) is most likely due to his confidence in Broly being the invincible Saiyan of legend making any power up not a surprise, but an inevitability in his eyes.

5) What's with the fate/destiny stuff about Goku & Broly?

There isn't really any "destiny" for their history, which is purely by happenstance.

As for an explanation as to why Broly is so fixated on Goku, the best explanation to rationalise that and his goals would be that seeing this low-class Saiyan born with a battle power of 2 having lived a good life and achieved such power through his efforts whereas Broly's natural talent that would suggest greatness was destined for him was rewarded with being stabbed by a paranoid king and having his innate gifts restrained for years by his father. Adding to this, we have Paragus saying to Vegeta the reason the prince is so scared of Broly is that being raised in Saiyan society he is more instinctively aware of the threat Broly poses. With that logic in mind, it can be rationalised that Broly's hatred for KAKAROTTO crying isn't as ridiculous as it sounds on paper and was more to do with him being aware of the potential Goku had, with Broly's innate potential being the embodiment of the Saiyans' savage, primal nature explaining why he'd be that in-tune with this instinct.
Unfortunately, the film did a fairly poor way conveying this pretty good idea and the sequel didn't help.

6) How happy was Takao Koyama when Broly really turned-out to be higher than Bills, just like he'd like to have thought before?

He'd probably be more happy if it was his original Broly and not this rag wearing space hobo that doesn't even have any cool one-liners

 

[Fantastische Hure]

So Broly (and by extension Paragus or Broly's mother) is a descendant of the previous SSJ?

Paragus only started restraining Broly's power after Broly punched his eye out though. He was already out of control as a child as seen in the flash-back, but then he seemed to go to sleep rather peacefully and was like "father" before Paragus tried to put the device on. It's like two personalities, which I think there is a name for (not personality disorder thing) but maybe it was psychopathy or something-else.

 

[Captain Cadaver]

So Broly (and by extension Paragus or Broly's mother) is a descendant of the previous SSJ?

Probably not, considering Paragus wasn't treat as the kind of super-elite you'd expect if this was a genetic thing. It's more likely that if there's some mutation to cause the LSSJ transformation, it's one that randomly appears regardless of genetic history.

Paragus only started restraining Broly's power after Broly punched his eye out though. He was already out of control as a child as seen in the flash-back, but then he seemed to go to sleep rather peacefully and was like "father" before Paragus tried to put the device on. It's like two personalities.

Indeed, though restraining it to the extent trying to access it would cause pain to Broly didn't do much to help Broly's condition in the long term.
Broly's first instance seemed to be purely instinctual and without rationality, much like his DBS self, so it could be seen as an accident. This is a far cry from his personality as a LSSJ in which he clearly conversed with his foes and would make grandiose declarations of his power and their fate in a manner fairly eloquent of a berserker. I'd say it's more accurate to say Broly's personality in the form is his dual-nature being combined, his rational and methodical side unleashing the savage nature that was hidden away.

Also, it's important to say Broly's peaceful nature after his sudden SSJ burst was before Paragus put the crown on him, essentially putting a leash of sorts on what urges he may have.

 

[Fantastische Hure]

So Broly was always going to turn-out the way he did, whether King Vegeta did what he did or not? Sad

 

[Captain Cadaver]

He had the nature to do so, though King Vegeta and Paragus' actions certainly propelled the evil side of him. Without the negative affects of their actions having an impact on Broly's personality, he'd probably be more of a destructive berserker similar to his DBS self rather than a clearly sadistic villain.