Sure, Kakashi is present in the Boruto manga. His role might not be as prominent as in the Naruto series, but he still has significant moments and interactions.
Kakashi is very much alive in the Boruto manga. The manga doesn't include his death. Maybe you got some misinformation or confused it with another character's fate. But for sure, Kakashi is around.
Well, Naruto could mimic Kakashi's calm and collected demeanor during fights. Kakashi is known for not getting flustered easily. Naruto might start to hold back his usual exuberance and be more stealthy, like Kakashi sneaking up on enemies. He could also try to use a variety of jutsu in quick succession, similar to how Kakashi combines different techniques smoothly in battle.
Well, Kakashi might introduce Naruto to more strategic ways of fighting. For example, he could teach Naruto how to better analyze his opponents before attacking. Naruto, who was previously more impulsive, may start to hold back and look for the right moment to strike, like Kakashi does with his Sharingan.
No, Boruto is alive in the manga. The plot hasn't led to his death. However, the manga is ongoing, and anything could happen in the later developments.
There are several fanfiction websites where you might find such a story. Archive of Our Own (AO3) is a popular one. Just go there and use the search bar with relevant keywords like 'Naruto banished fights Kakashi'. Another option could be FanFiction.net. However, it might take some time to sift through the results to find exactly what you're looking for.
Kakashi's training might make Naruto more strategic. For example, instead of just relying on brute force with his Rasengan, he could start using it in combination with feints and misdirections. If Kakashi teaches him how to read an opponent's movements better, Naruto can time his attacks more precisely.