Are those sentences are messages from your friend on LINE or something similar? もう学校かな is a question to you; "Are you at school now? / Has your today's class already started?" I guess your friend might have worried what if his/her message would disturb you attending in the class at school. Then, what he/she wanted to tell you is "最近パーマかけたよ/(Please refer to Eigo no Sensei-san's translation.^^)" Hope this makes sense.

"もう学校かな？" The meaning of this really depends on the context, because the only content words are "もう already/soon" and "学校 school". "かな" means something like "i think/wonder/maybe." We need to fill in the subject based on the context. But it could be something like "He/she has already started school, [i wonder]" or "school has already started (vacation is over), or has it?" "最近パーマかけたよ" "I/he/she recently got a perm hairstyle"