*pass you a box of tissue*
Yes, it was sad and unfortunate for both Kaiden and Gale :') They're like us; both of them has a story to tell and both of them are just trying to find their happiness--I have so much I want to convey through the two of them, so it makes me really happy to see you pay attention to the smallest detail! >///<
Yes, Gale is a quietly petty person lol. That's the perfect word to describe him x'D
And you guessed their hobbies already, but I'll explain more! Kaiden has fondness for music because amidst his busy training, trying to win the nobles' favor, the audience with the King, and schedule as the captain of the 7th Knight Division... the only entertainment he finds & enjoys is listening to Hototo's/a bard's music. It gives him a moment of peace and makes him forget his problems. The stories told by bards are also interesting to listen to.
As for Gale, he's naturally good at drawing (example: him drawing Kaiden facing the dragon). But he's not particularly passionate about it.
He draws because sometimes, he will need to make a report about what kind of new creatures they encountered to the King during their patrols (as the legend said, it's a sanctuary so new creatures would pop up now and then. The purpose of the report is for documentary and to decide whether the new creature is a threat or not) or when there's a thievery, he's the one who will make a sketch of the suspect's face. So yes, drawing is more out of necessity than passion. He has a talent for it, but Gale doesn't believe it's good enough to make a living with it.
As for teasing, once they get to know a person better. Kaiden and Gale will be fine with both receiving and giving. They had their fair share of teasings from Sir Marco and Vivian. You get the gist with Sir Marco, the woeful father who is 'abandoned' by his boys once they grew up. As for Vivian... well... if the scene in the hot spring is not enough hint. Here's a bonus scene I just thought up from a short video I watched on YT that reminded me of Vivian: When Kaiden & Gale were changing their clothes in the soldiers quarters, they heard a shout: "SHUT THE DOOR, THERE'S A FEMALE PERVERT!" and they saw a glimpse of a redhead, before the soldiers slammed the door. She's a pervert and her teasings are very bold so yeah, they're not innocent lol, they're actually quite immune by now and found blushing girls quite amusing since they're used to Vivian's boldness.
Your last question is a tough one though :'D
In the event that they both have feelings for the same person, they will definitely compete fair and square. But Kaiden will be more active than Gale in the matter of pursuing, because Gale believes Kaiden to be a better choice than him. While they have similar backgrounds, Gale is not confident in his looks because he once heard people describe him as 'gloomy' and 'Kaiden's shadow'.
Both of them will be loyal to their partners though, so I'm afraid polyamorous is not an option ^^; not to mention they consider themselves as brothers and there's an unspoken rule about not touching your brother's woman. They will not share their partners. Period.
In the case they compete and one of them loses, the losing one will back out and take some time to sort out their feelings. They will need some space, but the brothers' bond is stronger than anything else and what matters is the person they love is happy. At the very least, they'll know their loved one will be taken care of, after all, who knows their brother better than themselves?
I hope it helps! ^.^)/