I have created email contents as an html page. I have placed 4 check boxes and every time one of them is checked I want to run ajax which calls a url with parameters. Is such a thing possible or the email client will not run it for security reasons or/and other reasons? I can do it with a link to a page with the same contents but the recipient may not bother to click the link. The whole idea is: Can we run ajax calls in html email contents as if the contents were in an autonomous web page?
No you can't. All JavaScript is stripped from emails for security reasons. The best you can do, as you've listed, is to have a link in the email with parameters to allow the landing page to do it.
You can achieve interactivity, however, with checkboxes - such as hiding/showing content (already placed in emails). If you're already inserting the parameters, I'm assuming then you have the information--so place that content hidden in the email, which when checked, shows. Mark Robbins shows how it's done: https://www.webdesignerdepot.com/2015/10/punched-card-coding-the-secret-of-interactive-email/ (if that's what you wanted, let us know in the comments and/or include your code and we can give a tailored example)