Can I delete the critiques I've written?
No. Once you've sent off your critique, it can't be removed, any more than you can delete email you've already sent out.
If you and the author that you have sent the crit to both agree to delete it, you can send a message to moderator, but you should consider your crit the joint property of you and the person that you critted once you've sent it out.
Likewise, the person receiving the crit cannot delete or hide the crits she/he has received.
If you want to delete a critique in progress, go to Stories, click on My Critiques and then choose Critiques in progress. On this page you can abandon your crits in progress.