Since zero value transactions do not require a signature, I assume one can send 0 value tx from any address, even if he does not own the corresponding seed.
Is this assumption correct?
Technically speaking, a zero value transaction (bundle) neither needs to have nor can have a sender address. (Sending transactions in a bundle have
value < 0 and receiving transactions have
value ≥ 0).
That being said, you can send zero value transactions to any address. No funds will be moved and the address will not get added to the next snapshot either (unless there were some non-zero transactions as well).
The address does not need to be valid either (it only needs to be a valid Kerl hash, but the hash does not have to be from a valid private key), which is utilized by MAM and by the reclaim process.
Yes, this is indeed the case. When you use a spammer to create transactions, they will always have a random address.
MAM uses addresses as a message ID for example, as these data transfers are also zero-value. You can take a look at their blog for more information https://blog.iota.org/introducing-masked-authenticated-messaging-e55c1822d50e