If I use AES-128 in CBC mode, and I know the plaintext, ciphertext, and length of the plaintext padding, which is 15, can I retrieve the key and IV, using brute force or some special techniques?
No, the AES key is protected by the AES block cipher at all times. Only if the block cipher itself gets broken, if the implementation of the block cipher leaks data (though side channel attacks) or if the key is otherwise leaked can the key be retrieved by an adversary. Actually, even if the adversary dictates which plaintext is encrypted, the cipher should still be secure (CPA level security).
The IV is not considered a secret. That means that usually the adversary is allowed to know the IV value. And commonly the IV is simply send with the ciphertext, meaning that the adversary just has to eavesdrop the message containing the ciphertext to learn it.
It is possible to completely hide the IV, but this would not give you any security benefits (the IV is only used for the first block anyway when using CBC mode). The IV could be retrieved by a plaintext oracle attack, where available. However, the attacker could then retrieve the message as well and learning the IV would not give the adversary any additional benefits.