Can I sign or can the recipient encrypt a message with it?
In theory, you can, but practically...
Will an email client allow it?
...an S/MIME compliant software will reject an expired certificate. The sending client will reject to use the certificate. On the receiving side, an expired certificate is valid if the message was created before the certificate had expired (but that is not the case you constructed). With regard to a revoked certificate, the client should reject it, but not every client checks revocation lists, as far as I know.
If it is possible, will the message be rejected by SPAM filters?
No, I have never come across a spam filter that checks S/MIME certificate expiration or revocation. To the contrary, spam filters usually check the message content which they cannot do for encrypted messages.
And what about the messages signed and encrypted by self-signed S/MIME certificates? Are they treated as ordinary messages by the mail server?
Yes, as the mail server does not care about the mail contents.