Prepare for a long explanation and I may be wrong about some of this so if I am wrong feel free to correct me on it because this is just my viewpoint.
I Believe Tatsuya can use magic, but because he was born with an OP healing magic known as Regrowth that can restore the body to its original state from that point to 24hrs before, search magic known as Elemental sight and Decomposition magic (in other words he can break down both other magic and people) it means he can’t other magic freely and when he does it takes him a long time to cast it. He also has a seal on him that when unlocked by his sister allows him access to his full reserves of psions (which I think is another way of saying magic power) but we don’t know if this affects his ability to use normal magic as we never see him using any (in the anime anyway) also the reason his cast time is so long is because his special magic takes up a lot of space his magic calculation area which is like a storage space for magic sequences
Because he was born with an inability to freely use magic due to being born with Regrowth and Elemental sight he was experimented on when he was 6 by his mother and his aunt so that he would be able to use other spells and wouldn’t be affected by the in balance of his special magic. But we never see him using normal magic because in the anime he only uses decomposition, search magic and magic equipment like his silver horn, the third eye and the flight suit that are equipped with the spells to save him the time of casting them. Also due to the experiments on him he is able to read a magic activation sequence as a spell is being cast.
As for the relationship between the two siblings, in the anime it’s quite clear how Miyuki feels but as for Tatsuya I think he also low key knows that she feels that way but I’m sure he doesn’t feel the same way.... yet at least. But either way he still cares a lot for her.
Don’t read any more of this paragraph if u don’t want spoilers. As for the LN I haven’t read up to this point yet but it says on his character page that Miyuki is his fiancée so that’s kinda all that needs to be said (Incest Confirmed)
Shiba is their Fathers surname so that would be why and I assume their father married into the Yotusuba family which is a prestigious family rivalling the 10 master clans which is why their mother kept her surname
Apologies but for the incident in Okinawa I can’t remember what happened or what it was about
Sorry for the long explanation but hope this helps :)