Is there a data signing server with a verifiable time stamp?

Question

Is there a server that can help in the following scenario:

1. Alice (a client) generates some data (a hash of something)
2. Alice sends the data to the server in question
3. the server appends Alice's data with the current time stamp (i.e. UTC)
4. the server signs the resultant object with the server's private key
5. the server sends/responds to Alice with the signed object

As a result, Alice now can prove to Bob (or anyone else) that she had the hash at the time of the time stamp. Note: the server's public key is publicly available.

Answer 1

You just described RFC 3161 based time-stamping process.
See this older answer for list of free servers.

Answer 2

Take a look on this list : link.

But be aware, that the provided timestamp services are free, therefore I do not think they produce qualified timestamps.