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No, you can't max out both Heart Containers and Stamina Vessels in Tears of the Kingdom. Even if you complete all the shrines, dungeons, and quests that offer these upgrades, you'll still be two short of maxing out both. It's a bummer for completionists, but it's not a huge deal, especially if you're using all the awesome cooking and vehicle-building features of the game.
There are 152 shrines in Tears of the Kingdom, giving you 152 Lights of Blessing to spend on upgrades. You need 29 Heart Containers and 10 Stamina Vessels to max out both, which adds up to 39. So, you'd need 156 shrines to max out both. But, there's only 152 shrines, leaving you just short!
It depends on your playstyle! If you're a combat beast and want to take on the toughest bosses without a second thought, maxing out hearts is the way to go. It'll give you plenty of HP to survive those tough battles. However, if you're more interested in exploring Hyrule and don't really care about the hardest bosses, then you'll probably want to focus on stamina. You'll need a ton of stamina to climb, swim, and sprint all over Hyrule.
That's a tough question. 20 hearts is probably more than enough to beat the game's final boss, but it's always nice to have a little extra HP. Plus, you can use temporary heart-granting food to boost your HP temporarily, so you don't have to max out your heart containers. But, if you max out hearts, you'll be sacrificing a lot of stamina upgrades, which could be helpful for exploration.
You definitely need to level up your stamina to get the Master Sword, but maxing it out is not a necessity. It's really useful for exploration, especially if you don't want to constantly be using food to refill your stamina bar. However, if you're good at using Zonai Devices, you might not need to max out stamina. Those devices can help you get around Hyrule super fast!
Sadly, no. There are no plans for any DLC that would add more Heart Containers or Stamina Vessels. It's been the same in Breath of the Wild. Even with the Champion's Ballad DLC, you still couldn't max out both stats.
You got it! It seems like Tears of the Kingdom wants you to have a good mix of heart and stamina, and they even give you ways to make up for missing stats with temporary boosts from cooking and the like. It's like they're saying, "Don't worry, you don't need to max everything out. There are lots of ways to succeed!"