Does decryption with a wrong key creates a new encryption?
In general this is a moot point, as modern encryption schemes are designed so that the recipient knows if they have used the correct key or not. It is an interesting question to ask about encryption primitives, like a block cipher. Put more precisely, you are asking whether there is always a $k_3$ such that
$D_{k_2}(E_{k_1}) = E_{k_3}$
This is essentially asking if encryption forms a group, and in general the answer is no. See e.g. Is Triple-DES a group?. There are notable exceptions. You've seen that Caesar cipher is one, and Vigenere is another.