Hi Selina! As riding muscles you in a static way and during a long effort, I also do pilates to extend my muscles and stretch. Stretching sports and others such as cycling or swimming are great complementary exercices to riding :)
Yes, 100%.... core strength, back and shoulders, and cardio fitness are all important for riding! I like to do a mix of ab work, erging, and cardio.
I've seen a lot of benefits from working out, from increasing my stamina to improving leg strength and muscle control to even helping me get a better handle on my asthma. Of course, I've been a bit of a fitness junkie my whole life, so my opinion is probably pretty biased.
I like doing yoga, jogging, and a little bit of weight lifting. I also tend to focus on my core and leg strength, so squats and Russian twists are my favorites. Dance is also another great option, and there are a lot of choreographers on YouTube who post workout videos that you can follow along with. It just depends on what you feel like doing and how much time you want to dedicate to it.