Is it insecure to encrypt the wrong plaintext?
As long as you're using any modern encryption algorithm (and you're using it correctly: random key, new random or unique IVs for each message, depending on the mode of operation, etc.) then you'll be fine. In fact, you'd be fine even if an attacker got to choose which plaintext you encrypted and got to see the result; this information would not help him decrypt other ciphertexts. (This is a chosen-plaintext attack, and any standard encryption algorithm can withstand one. Unless you consider ECB a standard encryption algorithm. Don't use ECB.)

There is, however, a possible exception to this rule that might relate to your third question. If you accidentally encrypt a plaintext that includes your encryption key, then in theory this could lead to problems. At least, one could no longer prove the system's security under standard assumptions about the blockcipher.

If your third point was asking "What if I use the wrong key?" then, yes, this is a problem. They key you accidentally use might be brute-forcible. For example, a 128-bit AES key consisting of 16 ASCII hex characters (0-9, A-F) permits only $16^{16} = (2^4)^{16} = 2^{64}$ possible keys.