So, I spawned in the middle of a forest... got killed by a pack of zombies, then I build and small room made of wood, which helped me to stay alive.
After that,I decided to go across a small mountain and there I found water, flat ground and flowers, it looked nice so I decided to stay there.
Began hollowing out the mountain to make rooms inside, which quickly mutated into a small castle-like building, I found a mine, some cows and sheeps... and after 30 or so hours I haven't moved from that spot, and just kept building and refining my building to turn in into a nice castle with towers, a water pit and a big wall.
However I don't know if I should be doing something else... my better tools are only iron, sleep in a simple bed, and eat the bread I make from the wheat I haverst manually, but I keep hearing about diamonds, potions, and other interesting things. Am I playing the game wrong? Should I be exploring the world? I'm a little confused here.
There is no "Playing the game Wrong". Everyone's game and approach to it is different so don't worry about that, just enjoy it.
Finding and recruiting some livestock is probably your next step and you can always hope a zombie will drop a carrot or potato to vary your crops. You can find pumpkins, melons, and sugar cane growing around or find seeds for the first two and beets in mineshaft chests. You probably will want to go down deep and get diamonds soon as that opens up a lot of new things and then go to the nether to get stuff needed for the later game, but look around on the web for some of the many YouTube videos if you're needing ideas.
If you are enjoying yourself, you are playing the game right.
If you open the pause menu and click "Advancements", you will see a lot of icons with tasks that you may or may not have completed. They can help guide you towards learning what Minecraft has to offer (such as crafting new things, or using some items in specific ways), but they're just optional side objectives. The main objective of Minecraft is what YOU want to do.
I agree about playing whatever way you find enjoyable.
But diamonds make much better tools and armor than iron so if you are mining anyway you might as well do it down at the bottom of the world where the diamond ore is. Just be aware that there is much more underground lava below level 10 as well so bring water buckets and be careful.
Level 10 is generally a good place to mine, any higher and the diamond ore peters out, also that puts the lava lakes just below your feet so you're unlikely to drop down a hole and be unable to climb out of the lava.
The Wiki, 5th button on the green menu bar at the top of the page has a wealth of useful information.
You can look up things you are wondering about, like potions, and find out how to make them.
I was expanding my castle, and while replacing the floor, I fell like a mile down and died... right under my house there was a gigantic cave with huge vertical walls and water in the bottom, a very strange place. At least I was able to recover all my stuff.
It seems strange that such places can be right there under my feet, the worlds in minecraft seem more complex than I thought.
What you are describing sounds very much like my early games. You are exploring and learning right now, albeit on a newbie level. Eventually you will feel you have explored and learned as much as possible from your local environment and then you can venture further.
The advise above to dig deeper is good, as it does open the possibility of finding diamonds, (among other things), which can potentially take your game to the next level. But that is entirely up to you. You may still be discovering new stuff around most every corner at this stage, so the 'need' for diamonds or to move beyond your immediate home may not yet be necessary.
When I first discovered Minecraft, I played for several weeks without knowing about maps or villages or diamonds or horses and a great many other things. I had a blast as everything was new and each new find, (wool, flowers, fishing rod, etc.), opened up new things to explore and learn about the game. I encourage you to enjoy your time as a newbie in Minecraft, you'll never get it back.
There is no wrong way to play minecraft, but there are so many things to discover, like villages, temples, ravines (the cave you fell into), the nether and even the end. All of that can only be found if you venture into new areas and explore.
I play Minecraft but...last time when i joined the nether I spawned right on the nether fortress.After some time i came to kill blazes to get rods and make eyes of ender.Somehow skeleton (normal one) teleported from overworld through the nether portal shoot me,I fell into lava and thats it.Thats the moments when i realised that Minecraft Survival is not everything about GO KILL THE DRAGON!. Of Course you need to explore the ravines,caves,biomes,temples,...But now i just use Minecraft survival to kill mobs,harvest,maybe ill make a farm but iam not so sure (cow farm,sheep farm,...)and i gave up of going into new dimensions (till i dont get enough stuff to really do something in nether).Hope this helped you.
I recommend building a simple mob farm (for a good source of early game loot) and building a proper mine that goes down to bedrock (to be strip mined for precious resources). Both of these are cheap and easy to make, if you need help there are plenty of quality youtube tutorials. Just remember that neither 'need' redstone to work. The only reasons why I as a player would explore is to find villages and outposts or if I need certain blocks for builds or farms. Other than that exploring would not help you much for the risk of losing your base. Villagers are essential for the late game so locating a nearby village would be ideal. For good loot and resources world generated structures are unreliable at best. In short, keep expanding and upgrading your base.
Everyone plays differently, so you can't do anything wrong. You needn't take any of the advice offered here as long as you are enjoying yourself. I recommend watching some beginner tutorial series on YouTube just to get basic ideas of what is possible. Pick out the things that appeal to you. For example, if the idea of having automated farms appeals to you, have fun building some. If you prefer to harvest resources manually, keep doing that. You can spend months in one single place if you decide to turn your base into a masterpiece and build a village around it. You will find that your need for resources will dictate that you do venture afar to get things that aren't available in the immediate area. Just don't forget to make note of your coordinates (F3) or leave a trail of torches or something else so you can find your way back to your base. You can also switch to creative mode and let your imagination run wild. Most importantly, have fun!
You should fence in and light up your portals to keep mobs from using them.
Mobs can't use the portals to teleport to where you are, unless you are playing in multiplayer so that some other player keeps the other world active and the mobs from despawning.
But mobs can teleport to the Nether, say, while you are in the Overworld and since the Nether won't be loaded they can neither despawn nor wander off so they will be waiting for you if you use the portal.
As far as reaching the end game, I intentionally do not stray from the original spawn point that far, but find the nearest plain with cows or the nearest desert and basically stay there forever. This way, it's far easier to farm for leather for books (max enchantment) or to find endermen for ender pearls (to reach the End). If I don't have other resources at hand then I don't really import them, I just build small camps. For the most part, everything you will need to find is within 2 km of the start point even in Java so you can just diamond/spiral outward from the origin if you're looking for something specific.
When searching for the End, I will use the coordinate system to triangulate where I think the portal is - not sure if you consider this cheating, but it's not really possible AFAIK without specific coordinates.
Typically using these tactics I can comfortably "complete" the game (kill the dragon) in about 3-4 in-game weeks (about 6-8 hours).