I'm not sure of the exact grammatical explanation, but it's correct. The first clause refers to the subject, however it comes before the subject, which can be a little confusing. You can think of it as having an 'understood' subject and verb in the first clause, if that helps make it clearer. Although (he was) happy in the new school, he missed his friends" Similar examples: Although tired, they finished the marathon. Although intelligent in general, he was stupid when it came to relationships.

Consider: It was sunny and cold. It was sunny but cold. It was cold but sunny. Although sunny, it was cold. Although cold, it was sunny. The 5 statements describe the same weather. But the different statements convey differences in what the speaker thinks the weather should be and what the speaker thinks is most important about the weather.

Yes, it is an excellent sentence that is easily understood. "Happy in the new school" is an adjectival phrase that modifies the subject of the sentence, "he". "Although" means the same here as "in spite of being", "while", or "even if". I am not sure what part of speech I would consider "although" to be. The dictionary tells me that "although" is a conjunction, but that description does not feel right here. To me, it feels more like an adverb modifying the adjectival phrase.

In my opinion it is correct

Hye Molly Can we discuss and learn something new in English?