On the one hand, I hear people saying that the two keys are totally interchangeable, the first one will decrypt what the second one encrypted. This makes me think that the two keys are interchangeable.
But on the other hand, RSA generated keys appear to have different length, and on another topic encrypting with a private key was called “signing” and was deemed less safe than encrypting with a public key. (2)
On top of that comes the idea that the private key should be kept undisclosed when the public key should be openly distributed in the wild. (3)
I planned to receive data from an unique server, so my idea was to keep a public key on that server to encrypt data, and distribute a private key to all the possible customers, but this goes against (3). Conversely, if I distribute public keys and encrypt my data with the private key, the encryption is less safe according to (2).
Should I distribute a public key and encrypt with a private one to satisfy (2) or the other way around?
NB: in my case, performance is not an issue.
Your public key is used to encrypt a message, your private one to decrypt it. Thus with the public key, which you distribute, anyone can encrypt a message safe in the knowledge that only you (or someone with your private key) can decrypt it. To answer your question directly, no they are not interchangeable. You should never distribute your private key.
If you want to share a key with multiple possible customers, then there are really two options. Either you abandon asymmetric cryptography and find a secure way to distribute a symmetric key, for use with something like AES instead of RSA, to each of them, or you ask each of them to generate a key pair and provide you with their public key. Then you can decrypt what comes from the server, and re-encrypt for each customer. The number of customers will help dictate your choice between the two.