Is a different encryption and decryption algorithm used for every secret key, or can I use the same encryption and decryption algorithm for different keys?
You can use the same ones (which is good, because otherwise you'd run out of them pretty fast). In fact, when a cipher allows you to choose a key, that's basically the same as giving you a new pair of encryption/decryption algorithms for every key.
Usually, when designing a system that uses symmetric encryption, a small set of ciphers are used. For example, the popular NaCl library only uses Salsa20+Poly1305 and AES-GCM.