Thanks for the chapter!
Reason Lizel so shocked about MC being woken up by Arcana is that it's very rare for candidates to hear the voice of their Arcana, and the thought of him using it like an alarm clock is shocking because it's tantamount to a person using the ultimate and most powerful computer in the world as a cheap alarm clock. As for her turning away when finding out Arcana doing so on it's own is because it's a sign that not only is MC's compatibility with the Arcana unusually high but that the Arcana itself really likes him and is jealous. Don't know why but Lizel is head over heels with MC so holding back her lust and feelings so can appear as a proper, noble lady to MC and retain a great impression. Otherwise would be flirting and holding on to him even more than Miyabi. Thus, gets really jealous of others showing him affection as wants to monopolize position of main wife with him. Speaking of which, MC should really be considering implications of why he needs a bodyguard at all times to point where Lizel offers him a ride to school and Miyabi watching over him in class.
Btw, LN descibes it better but the 'Sprinklers' aren't fire prevention measures but drain and absorb hostile magic. So since MC's fire was magical it was put out by having all the magic in drained out. After all, magic comes in water, air, earth, light, dark, and non-attribute so need something that can handle all magic types as wouldn't have enough room to install a formula or circle for each type in an area much less keep them from interfering with each other. Also, everyone's uniform has special formula and spells put in to help protect them. So while a lot of unfortunate desks, chairs, pens, pencils, books, and miscellaneous possessions were destroyed nobody was killed and at worst suffered some third degree burns. Otherwise Sanjou who took the spell point blank would be in several pieces with first degree burns rathe than hunched over with his rear sticking out.