In portrayals of kings across cultures, it seems that they can always be found sitting on their throne, or occasionally leading a an army into battle. How realistic are these portrayals?
Hi, not discouraging direct answer to your questions, but while you're waiting, you might be interested in some earlier threads
Thrones and throne rooms
What did monarchs actually do with a throne and a throne room? Were they purely for ceremonial purposes? /u/grashnak gives a quick intro
Were "throne rooms" purely ceremonial, or did kings actually spend hours a day just sitting in one place? Surely there must have been a better way for a king to spend his time. /u/Tiako discusses Ancient Rome
Did an Egyptian Pharaoh wake up in the Morning and sit on his thrones all day? /u/LivingDeadInside discusses Ancient Egypt
What do Kings in the medieval times do in their spare time? /u/ComteofStGermain and others discuss what else there was to do in Medieval Europe
Leading battles
yup, that was and still is a thing. A question came up just the other day Who was the last king to take part in combat while they reigned? featuring /u/thejucheisloose
What are the most contemporary examples of Kings/Emperors/Governors/etc directly leading armies in battle? When did this cease to be common practice? /u/jedav on the decline of the practice
/u/iphikrates on Classical Greece Back in the time of sword and bow, did generals actually fight in the front lines?
an old thread with several examples Did Medieval kings/lords really lead the charge?
Did kings actually lead troops into battle often? /u/mizzamir gives the examples of a few English kings
.. and there are many other examples. A search of king (or monarch) + lead* + battle will turn up many posts