Can you please tell me how to check whether the highlights are blownout when the sky is plain without clouds and dark blue??

Some cameras have a setting that'll show you any blown out details when you take the photo -- usually the affected areas flash on the camera's display. On my Canon the option is called "Highlight alert", selectable on one of the playback menus. So if you're looking for a general tool that you can use while taking photos, that's a good one to know about.

Just looking at the image histogram is another quick way to detect blown out details. The brightness histogram shows you the distribution of pixels in the image, with darkest pixels (black) on the far left and brightest pixels (white) on the right. If the histogram indicates a large number of pixels at the far right, that means blown out highlights. Most cameras can display such a histogram for you, so that's another tool to use while you're shooting. Photo editing software can usually show a histogram as well. Here's one from Apple's Photos app:

This one shows red, green, and blue components, and you can see that there are a significant number of pixels where all three components are at or near the maximum value.

Please point out the mistakes or any setting changes that might have made this snap a better one.

The first thing that occurs to me is the subject... you've got a photo of overgrown vegetation that's just not that interesting. Incorporating some object to act as a focal point in the image might help the composition. For example, you could get a friend to stand in the photo wearing a red or yellow jacket to add a splash of color. They don't even have to be recognizable -- they could stand a bit to the side and with their back to the camera, so it becomes a photo of a person looking out over the hills. Or if there's a statue or a tree around, you could use those as a point of interest.

As @fkraiem points out in a comment, it's likely that the photo you wanted to take had a lot more blue in the sky, and perhaps the blue sky and green plants were attractive at the time. If that's the case, reducing the exposure a bit might help keep the blue sky, although the leaves would likely be darker. Time of day can have a huge impact on this kind of photo: if you shoot in the early morning or late afternoon, the sky won't be as bright and you'll have an easier time getting a beautiful blue sky while still exposing the plants correctly.