So as someone who just got a Switch and Zelda last week, I have some questions if anyone could help me out. This game is so different from the previous Zelda games I feel at a total loss as to how it works sometimes.
1. Is selling items the only real way to get rupees? I get almost none ever from enemies, bushes etc.
There are other ways to get rupees, like playing some games/challenges, and they can be found in treasure chests, barrels, crates and under rocks.
2. Same question for hearts. Is eating the only way to get health?
Sleeping at an inn/in a bed or completing a shrine fully recovers your health. Also getting in hot spring water on Death Mountain recovers your health.
3. What is the best way to get new armor? I have played maybe 10 hours or so, and just got the Zora armor (my first divine beast mission so far) and it actually has less armor than the default blue shirt. Are there armors that have much more defense? I feel like the enemies hit really hard. In previous Zelda games it was like 1/4 or 1/2 heart per hit, maybe 1 full heart for heavy enemies. In this game I get 1 hit killed all the time, and get 3 or 4 hearts taken away all the time. Is the game always supposed to be like that? Given how resource intensive eating to regain hearts is, that seems a bit annoying.
Armors can be bought (make sure to check the clothes shop in every village), found in treasure chests, and given to you for completing quests. And pretty much all armors can be upgraded to increase their defense and add special abilities at Great Fairy Fountains. There's one behind/above
and three others in the world.
4. What is the best way to get around? I tamed a horse, but when I go more than 20 feet away I can't call it to myself anymore. I'm using the paraglider where possible, but walking on foot seems to take so long. I feel like sometimes I play for an hour and get literally nothing done.
I didn't use horses much. You can shield surf when going down slopes, but I don't do that either. I focused on upgrading my stamina early on instead of heart containers and that greatly made running, climbing and swimming much better.
5. Similar to the above, is there a way to figure out the best paths to get places? I feel like I waste so much time trying to get up hills and things because I have no idea if that's the way I'm supposed to go and there's a confusing amount of cliffs/hills/ ravines etc. on the way to anywhere.
Follow the paths/roads. Activate towers to reveal terrain details (including roads).
6. Does weapon durability ever improve? I go through so many weapons, it's a constant stress of inventory management to make sure I'm not wasting any spots on old/near broken/weaker weapons.
Weapon durability improves much later in the game. For now your best bet is to collect as many korok seeds as you can.
I know I get more spots from korok seeds, but when I turned one in I got... 1 space. Really only 1 per seed?
Actually the number of seeds required for each additional space inceases almost exponentially. So if you thought 1 seeds for 1 space is bad, you're in for a rude awakening 
7. Is there no jump attack like in previous zelda games? I know about the parries and stuff, but when I'm Z Targeting, is there no way to do the forward jump attack for more damage? Are there any other combat moves I'm missing?
There is a jump attack. You don't even need to be Z targeting to do it.
8. Does climbing ever get better? The speed is so excruciatingly slow and tedious, and from what I can tell having more stamina changes nothing except that you can climb longer.
There is a climbing armor set that greatly improves climbing speed. And one of the champion powers you get will allow you to create updrafts so you can quickly glide up at any point.
Forgive me if these questions are naive, but as a big Zelda fan who has loved almost every game in the series, I am just really confused about so many things in this. I want to enjoy it as much as possible, but I am afraid I'm just missing something here. I feel frustrated almost constantly when playing. It's like I'm not playing the same game as everyone else.
