I have some questions about staking and PoS system

Hello there! I’ve been staking my coins for a while after shelly hard fork and in this time i am trying to learn more about cardano. But there are still some questions i couldn’t find any answers. I hope you guys help me.

First of all i couldn’t find any useful information about how staking or proof of stake really works. I mean i watched some vidoes and read some things so i know the basics but i couldn’t see any technical information. If i have to ask 1 by 1 i can say

1-) To verify transactions why does this system needs other ADA coins? What is the technical neccessity of these coins and how these coins verify transactions? What does verify means in this context?

2-) Why there are 13 billion of ADA waiting in the official reward pool to distribute as rewards. I mean doesn’t that make this project some kind of cheap or insignificant? I’m okay with using fees and some reward budget to rewarding but 13,000,000,000 ADA? Come on!

3-) Why past transactions keep verifying? For example i have this transaction dated over a month ago and it has more than 217000 confirmations and it’s keep going. Why it’s keep going? Does it going to stop at some point? If not, doesn’t these confirmations keep the network busy or make it some kind of slow or something?

4-) What is the stake pools purpose? I know cardano community is huge and it’t getting even bigger by the day. So why don’t everyone decentralize it by themselves? Doesn’t that make it much more decentralized and efficient?

These are the questions i wonder for now. I would be appreciated if you can help me. Thank you already.

It is verified only once (not really true as a full node with full resync will do it again) by every pools, relays, Deadalus and other full-nodes. So, verified only once (or a few more times) by a full node, and that confirmation simply means distance from the block that transaction was stored. E.g. if your transaction was added into the block 1000000, and the current block is 3m therefore the confirmation is 2m, and that simply means you need to alter that many blocks to change that tx. For micropayments one or more tx is fine, but if you buy a house by ADA, then you should wait a some longer period to settle it down. I would say a stability window time if you spend millions USD.

Tx verification means, you have unspent money rightfully to spend i.e. cannot spend it twice and it was yours
And that means the system must be sure that is yours and unspent. Ownership is based on the spending key attached to an address (verifying key) the contains the amount ADAs, while for the latter your node (as all other full-nodes) have the list of all unspent ADAs (as tx and idx in th tx) to be sure that what you are spending is not spent already, so that is why. It is a bit more complicated and if you want to learn about it, search for UtxO i.e. unspent transaction outputs. Sorry, typing on the tablet.

It fulfils a simple purpose, secure the network on behalf you and other stakeholders, otherwise it would require almost every stakeholders (afaik at least 80%) who has ADA to be online 24/7/365 and ready for creating a block when it is scheduled ( and verifying every blocks), which is not achievable, therefore the concept of pools is make it for you by delegating your block forging right and therefore securing the network.

This is only for staking rewards and for funding the treasury (for future community voting based development) currently with a ~24% yearly inflation rate (mainly goes to the pools and the rest to the treasyry) as an exponential function which would last for about 150years, until the utilities (as tx fees) will be capable to compensate the pool operators effort for securing the network. You should check Cardanos monetary policy here. https://docs.cardano.org/en/latest/explore-cardano/cardano-monetary-policy.html
And some other sources.