Having watched the video she can certainly blow things up, but anytime she burns a person the fire always seems to original from outside. She can destroy vehicles from inside but I think that's due to their being empty space there for her to work her power. Can't really confirm one way or the other on that, but it seems that way to me.
As for her kinetic shield, what's the most it's stopped? Given the things Link's arrows can do, and the impressive strength he displays, I'd place his arrows well above conventional bullets, and the ice arrows themselves are powerfully magical. I don't think it's as cut and dry as she simply stops the arrow. Even if the physical arrowhead can't penetrate, the magic is enough to flash freeze molten lava, and it did render the interior of a volcano inhabitable, if the arrow goes off that close to her it could still kill her, imho.
As for how the Master Sword would interact with fireballs, I can't really say. The sword can interact with incorporeal enemies, cut through magical barriers, absorb and reflect lightning, absorb miniature suns, manipulate time, and do all sorts of other weird things. I think it should still interact with her power despite it being kinetically based, largely because the sword is sentient and magical, and magic doesn't traditionally interact exclusively with other magic.
^The spirit/personification of The Master Sword, Fi. She's the most powerful being still present in Zelda canon, since the deities who created the universe seem to have left.
So, I personally believe he could reflect the fireballs, but this isn't 100% provable. It seems the most likely outcome, though. Even if they do explode on contact, Link could take a few and the second would never Land. He has impressive combat speed and an indestructible shield.
As for her tactic of blowing up the ground underneath him, the Sword's protection does seem to have some range to it.
YouTube video
4:25
The Master Sword breaks a curse laid on Link without touching him. I'm not definitely sure how close her explosions could originate, but I think there'd be a small bubble near Link she couldn't really influence. shrug This is of course on top of the Iron Boots which probably weigh multiple tons, which he could use to make himself hard to move around. Even if she knocks him into the air, he has a glider of sorts to come back.
It could also probably cut through her kinetic field if Link came within range of her, and she'd be helpless then.
For me it comes down to Link's durability and experience against dangerous opponents. She's still physically a human child, and I haven't seen her go against a single enemy comparable to her own power (rather than normal humans in numbers). I may be uninformed, though. It just seems like a foreign situation for her to be confronted by someone who can rival her own power.
/Hat tip.