Although, the submitted form data shows up in the email section, I do not receive any email message as an admin although I have configured it to receive emails?
Since the Contact Form uses the default email sender provided by WordPress, the issue might come from your WordPress installation. Do you receive emails when somebody comments on your site, or when somebody registers?
When a visitor fills out the details, after submitting the form, she get the same page without getting a thank for contacting type of message.
That seems like a bug indeed: the contact form should reload the same page, and replace the form with the contents of the message you've just sent.
Could you post a link to your contact form so I can have a look at it?
How can I ask visitors to attach an image by using the contact form?
I am afraid that is currently not possible with Jetpack Contact Forms, but I like the idea! I have registered your suggestion, and we'll consider adding this feature into one of the next Jetpack releases.
In the meantime, you could add a new URL field to the form, so your readers can send you a link to the image, hosted on another site.