
I'm probably in the old, open-minded minority, but I don't see him as "sleeping around" at all. He didn't have anyone he liked, was into guys, started a no-strings-attached sexual relationship with his ex-tutor (please when he was legal) who I'm assuming was a friend of his older brother's. Now he's started to like Kanata and it's getting flirty, but he hasn't broken off with his sex friend yet based on a (so far) fragile romantic attraction. Nothing wrong there. This kind of slight overlap is common in real life so I don't see it as a problem.
As you guys have said the whole tutor thing is totally cliche - but I kind of get why it's such a trope. Who else was he supposed to meet? Straight high schoolers in BL have generally lost their virginities with past girlfriends, but what's a gay boy to do? Grindr??

No problem!! You're not dumb at all, languages have so many different ways of saying things, and English is weird anyway. I teach English to kids who speak it as their 2nd language, and a close friend of mine is an ex-pat and asks me questions like this all the time so I like answering!
In this case, the two phrases mean kind of different things. "No-strings-attached" sex would mean you aren't in a romantic relationship, you're just having a physical relationship and both would be free to sleep with other people. You can have a "no-strings-attached" relationship with a single person.
"Sleeping around" generally means somebody is having sex with multiple people (at least more than 1) - all of the sex could be casual or no-strings-attached, but you can't "sleep around" with just a single partner even if that one person is just a sex friend. One sex partner is not "sleeping around." You could also be "sleeping around" if you were cheating on your steady partner with other people, but you would have to be in a relationship for that to apply.
Controversial I don't know but then again its like I don't really sense that either side is doing anything to indicate they want a romantic relationship. Akira can sleep with whoever the hell he wants as long he's ain't a married or old man.