In simple words, we can say that the coins are on the blockchain and they will never leave it, and the hot wallet is just the door, which I must have it's key to open it.
In simple words, yes. You could say the coins are 'stored on the blockchain'.
A wallet is a piece of hardware/software (except paper wallet) which manages the private-/public keypairs for you.
A private key is necessary to spend coins which has been prior send to the corresponding public key.
that's means I don't have to worry if my phone damaged or gone to space as long as I have the recover key 
Thats true. But everyone else who gains access to your mobile phone (or more precise: to your private keys / seed) will also gain full control over your bitcoins.
You should try to never leave any traces (e.g. old mobile which you throw away or sell to someone).
Regard such seeds / private keys as compromised and don't use them anymore once they could theoretically be known by someone else.