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Rukawa isn't a big fan of PDA, but he doesn't hate it either. He won't be the one to initiate affection in public. However, he also isn't the type to slap away your hand when you're trying to hold onto his. I can see him simply shoving his hands in your pocket still holding onto yours
Rukawa is quiet by nature. He is satisfied with sitting and listening to you talk about your day, if-you-won't-ask-he-won't-share type of guy.
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I see him as a quiet tease, he needs no words to point out how much taller he is, elbow on your head and all. Oh, you don't like cats? He casually lets the one he is holding paw at your arm. Oh, you like cats? His eyes give you a side eye as two cats get closer to him and leave you with your hands outstretched.
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Rukawa has no reaction to you showing up to his matches, I can only see him giving you one glance before the play, so you better time it right to show him your support (maybe with a thumbs up and a smile?) even if he won't meet your gaze until after the match. Rukawa might not show it, but he definitely appreciates the subtle gesture.
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His first favorite dates is cat cafes. Pretty self-explanatory.
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He values his privacy so asking for relationship advice from ANYONE, let alone the Shohoku club, is out of the question.
The more time you spend with him the more you understand his thought processes and how it revolves around his naps, so yeah, tutoring will be adjusted to fit his style since Rukawa can't solve one equation without his head lying sideways on his arm and not to mention him taking a ten-minute nap before he moves on to do another subject. Between him and you, you have more chance to fall asleep for hours, since Rukawa always ends up waking up after ten minutes.
He is also a light sleeper and a clingy one too, good luck trying to get him off of you. His stubbornness shows up at the worst times.