About their relationship. BIG SPOILER!!
1. remember that Nunnaly said that the plaque never happen to her?Alves since really small has really bad plaque clive as he has really powerful magic. it was said that he is a founder class fire mage. Nunnaly actually have powerful magic too, it is hinted with how her hair changed to blue (one of the characteristics). So, Alves kind of make her constantly (average) mad so that her magic flows constantly not suddenly burst. That's why after her hair changing is the started when Alves 'teased' her, different to his indifferent before.
2. This is comes from the ongoing sequel. Alves has a memory of someone he cherished (as a child Alves is a lonely child because his constant burst of plaque clive) that he doesn't know where he get that memory. That someone told him that he is going to be a great wizard, and is going to have a rival that will accompany him (the rival will be his seatmate, how they will constantly fight with magic) etc. (basically someone told him about his future). At first when he saw Nunnaly, he kinda doesn't accept that she is going to be that rival but slowly he accept it.
3. Even though Nunnaly think they are nemesis, I think Alves thought she is his cherished friend. There is a plot around the ice magician, how some ice mage is danger etc. When Nunnaly's identity as ice mage get known by (suspected) enemies, Alves takes her identity. He disguised as Nunnaly with magic, Nunnaly at that time doesn't know. When she know that someone really hurt because of her, she comes to visit him, but then when it revealed that Alves is the one who got hurt, it is the first time that plaque clive happen to Nunnaly.
4. After the big war against some devils, Nunnaly heritage is revealed. With them, then she can't be a receptionist anymore. So, when Nunnaly told her wish to stay as receptionist for reward (for participating in war), the king already know it and Alves already ready to cast a really huge magic to make all people (save for really few) forgot about her heritage. So then, she can stay as a receptionist