Spending bitcoins costs me to sacrifice (i.e. can only be used once) a private/public keypair, am I right?
No that's not correct. Key pairs can be reused but it is not recommended for privacy reasons. All transactions are public and reusing the same address over and over again make it easy for people to build a profile about you.
Receiving does not use up a private/public keypair, am I right?
You need an address to receive bitcoins and behind that address is a key pair. But you can reuse it like I said above.
Creating a new address also uses up a private/public keypair, right?
When I spend bitcoins, how is this connected to my address, if it uses a new private/public keypair everytime, that has nothing to do with the original keypair of my address?
It doesn't use a new key pair everytime.
You need to read up on asymmetric cryptography. The gist of it is that the private key and public key are mathematically related. Bitcoin spend transactions are signed by your wallet using the private key and that signature can be verified by everyone using your public key. Private key does not have to be exposed in order to spend or receive bitcoins.
A bitcoin address is a hash of your public key and that hash operation is also repeated by nodes to verify that you indeed own the bitcoins and have the right to spend them.