Emo is a bit more than just lyrical content, otherwise almost anything could be emo. Stylistically, I wouldn't say FR are close to Emo, which itself was an offshoot of hardcore punk in the 80s, stuff like Rites of Spring, Drive Like Jehu etc. Then in the last decade or so it seemed to be incorrectly applied to weird (bad) metal bands who wear eyeliner and scream about girls. It has become a bit of a joke term and probably shouldn't really be used for anything now. The original wave of Emo bands tended to hate the term anyway. It's always been a little bit derogatory, I feel. I'd say indie rock is suitable, and they do have a fair bit of folk in there too, though indie is such a large umbrella term, which has also been bastardized from its original meaning.
The news is incredibly sad. I didn't know him, but I'm friends with a couple of people who did and it has hit them hard. When someone passes, it's natural to hear the whole "no one had a bad word to say about him/her" but I do know that was remarkably true about Scott well before this happened from those I know who knew him. It's tragic that someone, anyone, can be in such a position mentally to make that decision.
I quite like Frightened Rabbit, but I was never massively into them bar a handful of songs, though I really like Scott and Grant's new side project, Mastersystem. They just released their first album a couple of months back. I only heard it for the first time recently, it's a great straight-up rocker, early Idlewild-ish, one of my favourite LPs of the year so far. It's just so simple and driving, everything sounds big, it's a great listen, I'd recommend it especially if you like Scott's music. It's a shame we won't get to hear Scott make any more music. He was very talented. A massive shame.