No, that would be "revocation". Expiration is relatively easy to implement because the expiration date is known in advance and so you can simply put the expiration date in the certificate when it is issued. Revocation is relatively difficult because you need to continually check some database for revocation information — that's where CRLs, OCSP, and the like come in. And there's a lot of complexity under that hood, which, once the dust settles, boils down to just issuing very-short-lived certificates under a different guise.
No. The certificate's expiration is fixed at time of issuance. You could set the expiration of the certificate to the expiration date of the domain, but the domain could be transferred, cancelled, or revoked before the expiration.