2) the sender creates a new transaction broadcast it to the network until it reaches the miner...
Yes. (It reaches the transaction pools of all the miners.)
..that 1) verifies it,
Yes. The transaction must equate to a valid state transition.
2) includes it in a new block
Yes. They put it into a candidate block, then race to solve the proof of work for that block. If they are the first miner to solve the PoW, then their block will be accepted as canonical by the rest of the network. (We've jumped ahead of ourselves a bit here... )
3) executes the transactions of the new block,
They essentially already have, by checking the state transitions are valid and solving the PoW before anyone else. (Jump to the last part for a clearer explanation.)
and 4) finally sends the block to the rest of the network which verifies it and executes its transactions
Once a miner solves the PoW for the block, they propagate it to the network, yes. Everyone else then verifies the state transitions are valid, and the PoW for the block is indeed correct.
In verifying that the transactions equate to valid state transitions, they have, in effect, executed the transactions.
(also, I want to know here if the "rest of the network" executes the transactions of the new block or simply update their states).
I think the thing to get your head around is that "execute the transactions" and "simply update their states" is essentially the same thing. There's no distinction between "Okay, I've verified these transitions are good by applying them to my previous state..." with "... and now I'm going to actually 'execute' the transactions".
So the miner proposes to the rest of the network a set of valid state transitions around which the network can agree and form consensus on. Once everyone agrees that the state transitions are good, then the transactions have effectively been executed by everyone. The result of the transactions is the updated state.