Yoga would be great for your first point. Dynamic vinyasa is a good workout for the mind and body, and it can be complemented with yin yoga to focus on flexibility even more.
Yeah, yoga is something I am going to do, not sure which kind yet or if I want to attend classes or just do it solo.
I cant recommend Omstars enough for solo work. They have tons of material to help develop fundamentals, though Id encourage you to use the videos to build a habit and then seek out a teacher.