(sorry for my newbie questions
)
Since you are a newbie, please understand that the Bitcoin system at the technical level probably does not work the way you think it does at all. There are a lot of abstractions that the user interface uses to make it easier for us humans to talk about transfering control of value, and those abstractions often lead people to assume incorrect things about what is actually happening.
(For instance, at the protocol level, there aren't actually any bitcoin addresses or bitcoins at all, transactions get "sent" but they don't get sent "to a bitcoin address")
when I use an API
What API are you using?
to access a btc server
Are you running your own server, or are you using a service provided by someone else?
and request a new address to my wallet/account
Wallets and accounts are not the same thing.
If you are using a wallet, then you have exclusive access to your bitcoins. You are fully responsible for keeping the wallet secure and backed up.
If you are using an account, then you assign control of you bitcoin value to a business. The business takes responsibility for keeping control of that value secure and backed up. In exchange, they promise to assign control of an equivalent amount of their value wherever you ask whenever you ask. You have to decide if you trust them to keep that promise.
and then want to send some amount from coinbase for instance, I dont need to worry about it, right?
Correct. As long as you are using well written wallet software or a well run and trustworthy service for your account, then you just tell Coinbase what address to use. Coinbase then broadcasts a transaction that gives your wallet or service control over the bitcoin value.
I mean, how does coinbase send it to the right place?
You tell them the address to use. They create a transaction that re-assigns control of that bitcoin value to the entity that generated the address. The wallet (or service) you are using then uses the private keys associated with the address to re-assign control elsewhere when you want to transfer control of the bitcoin value from there.