I.. have to figure out which part's unpredictable here but okay let's see.
What we're shown during that whole arc is that he's steadily taking a bit more interest as the opponents become stronger. He still calls everyone trash, but there's some sense that he's beginning to.. maybe not respect them, but definitely see that they're not complete nobodies. So a situation that wasn't worth his time at all becomes something he thoroughly enjoys, once it's actually enough of a challenge to bother with.
He has a lazy, uncaring approach to things that look insignificant, but is capable of being swayed in his opinion. People have to actively prove their worth to him, basically. But even the Varia are "trash", so it's not as though he'll admit it...
Timoteo powering Gola Mosca is a pretty big twist in the story, so that might be part of it? What I see in that is thorough planning. He knew prior to coming to Japan that Tsuna was one of his opponents, and that making him out to be the bad guy would work in his own favour. Because the robot's not really a "powersuit" type thing, and the person inside is a fuel source as opposed to a pilot, it didn't require anything more than abducting Timoteo and forcing him in, and that gave him a chance to get back at him for everything. We see that Xanxus is capable of extreme levels of cruelty, even being willing to kill the man who was (or in his eyes only pretended to be) his father, if it gets him what he needs-- in this case, less competition and more respect from the family, as he'd be put in a position of looking like he'd avenged his death instead.
He's extremely self-serving. Anything he does for Vongola is only because Vongola should be his. His own interests will come first, when he has them. And when he does, they're almost always fueled by emotions-- violent reactions to whatever's currently making him angry or excited.
The fear at Tsuna being able to use the same freezing flame that sealed him before is most likely trauma. He'd already been frozen for 8 years, and definitely wouldn't want that to happen again. He had to take things as seriously as possible once he knew he was really in danger, but at the same time the fear and anger was keeping him from being able to act rational enough. Winning those rings would give him everything (if he truly had Vongola blood), and being frozen would take it all away, so he was under quite a lot of stress all at once.
If it's the laughing at Squalo's "death", I believe we're shown this just to add fear for the protagonists. He's a "villain" at the time, so it's likely meant to be seen as unsettling that he can care so little. There's various ways to actually interpret it. He might be impressed that Yamamoto was able to defeat him. He might see some level of comedy in that if anyone was to be killed by a shark, it was the one who's name is "shark" in Italian (considering a certain fish food comment). The event that's "now square" is never actually shown in the series. Squalo does have something over him, and he may also just be relieved that he's no longer able to use it. I'd left that out since trying to figure out what it was would end up reaching into headcanon territory, and definitely requires Squalo's player to have a ton of say in it, as well. But we do know Xanxus didn't become the leader of the Varia the "right" way.
/o\ 2 am is a bad time to be writing, so if there's something more specific just let me know and I'll try my best!
Re: REVISION REQUEST
What we're shown during that whole arc is that he's steadily taking a bit more interest as the opponents become stronger. He still calls everyone trash, but there's some sense that he's beginning to.. maybe not respect them, but definitely see that they're not complete nobodies. So a situation that wasn't worth his time at all becomes something he thoroughly enjoys, once it's actually enough of a challenge to bother with.
He has a lazy, uncaring approach to things that look insignificant, but is capable of being swayed in his opinion. People have to actively prove their worth to him, basically.
But even the Varia are "trash", so it's not as though he'll admit it...Timoteo powering Gola Mosca is a pretty big twist in the story, so that might be part of it? What I see in that is thorough planning. He knew prior to coming to Japan that Tsuna was one of his opponents, and that making him out to be the bad guy would work in his own favour. Because the robot's not really a "powersuit" type thing, and the person inside is a fuel source as opposed to a pilot, it didn't require anything more than abducting Timoteo and forcing him in, and that gave him a chance to get back at him for everything. We see that Xanxus is capable of extreme levels of cruelty, even being willing to kill the man who was (or in his eyes only pretended to be) his father, if it gets him what he needs-- in this case, less competition and more respect from the family, as he'd be put in a position of looking like he'd avenged his death instead.
He's extremely self-serving. Anything he does for Vongola is only because Vongola should be his. His own interests will come first, when he has them. And when he does, they're almost always fueled by emotions-- violent reactions to whatever's currently making him angry or excited.
The fear at Tsuna being able to use the same freezing flame that sealed him before is most likely trauma. He'd already been frozen for 8 years, and definitely wouldn't want that to happen again. He had to take things as seriously as possible once he knew he was really in danger, but at the same time the fear and anger was keeping him from being able to act rational enough. Winning those rings would give him everything (if he truly had Vongola blood), and being frozen would take it all away, so he was under quite a lot of stress all at once.
If it's the laughing at Squalo's "death", I believe we're shown this just to add fear for the protagonists. He's a "villain" at the time, so it's likely meant to be seen as unsettling that he can care so little. There's various ways to actually interpret it. He might be impressed that Yamamoto was able to defeat him. He might see some level of comedy in that if anyone was to be killed by a shark, it was the one who's name is "shark" in Italian (considering a certain fish food comment). The event that's "now square" is never actually shown in the series. Squalo does have something over him, and he may also just be relieved that he's no longer able to use it. I'd left that out since trying to figure out what it was would end up reaching into headcanon territory, and definitely requires Squalo's player to have a ton of say in it, as well. But we do know Xanxus didn't become the leader of the Varia the "right" way.
/o\ 2 am is a bad time to be writing, so if there's something more specific just let me know and I'll try my best!