From the developer tool, how can we find out which requests run in sync with the browser's execution thread, and which run out of sync in the webpage? and To check the performance of website which requests should be included for the performance testing of the website?
The approach should be the following:
Configure your HTTP Request samplers to download so called "embedded resources" from HTML pages, this will simulate real browsers behavior (1 main request to the HTML page followed by parallel requests to download images, scripts and styles). It can be done using HTTP Request Defaults configuration element.
here you can also exclude external resources to focus only on the application you are testing at the moment
Add HTTP Cache Manager to represent the browser cache as real browsers download these images, scripts and styles only once, on subsequent requests the resources are being returned from the disk cache.
If there are any dependent requests originating i.e. from AJAX calls they need to be added manually
See Web Testing with JMeter: How To Properly Handle Embedded Resources in HTML Responses article for more details.