Some things I still don't understand about Ethereum...

Hi,

After some digging I still don't understand some major stuff about Ethereum and I hope someone can explain the following:

1. The miners are executing the smart contract code - right?
Does all of the miners in the system execute all the smart contract's codes? And if so, how is the system able to scale and keep writing blocks every 17 secs when more and more contracts are being created?

2. In bitcoin, the miner that gets to write the next block get it because they where able to find the solution for the specific hashing problem - how does this work in Ethereum?
I mean, how does the execution of smart contracts code and hashing the blocks works together?

3. A DAPP is basically a collection of smart contracts that work together and sending eachother eth to run and do specific tasks - right?
If I got this right, what happens if someone else sends eth to one of the components (smart contract) that shouldn't run seperatly?

4. Bitcoin has a limited number of coins - how does this works here? When are ethers created and is there a limit? What are the rules?

Thanks again :)

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