I want to create a form in which when a front-end sets a date and on that date the post gets automatically deleted. Is it possible?
I will say, I don't exactly understand your words "when a front-end sets a date"...
I'm assuming wp-admin setup. Go find a post expiration plugin. There seem to be more than a couple of these out there. The plugin I've used ws "Post Expirator" Awesome tool. You can create a start posting and stop posting date when the post is created. I used it on a site that was advertising future events. You could create a whole years worth of upcoming events, and then schedule the posts to start displaying one month before the event, and they'd expire the day after the event. Way cool.
Obviously for a form, this will only work if the form is contained within the post, perhaps short code style?
If you want the site's users to be able to set something up an expiration date that is an entirely different conversation. I think that is do-able as a new custom plugin. Not easy, but do-able.