How can I set a End Frame of blender movie clip editor to match the end time of the video (without trying to search the End Frame of video)? Currently when I'm importing the video, the End Frame is set to 250 instead of ~600 which my video is currently having.
Your problem - from a VSE point of view:
Make sure, the function Use Preview Range is unchecked if you want your Scene Frame Range to be set accordingly for your final Render.
Further explanation regarding your situation:
You want to achieve this in the MCE directly. Which is possible via some Python code. But for a quick manual workaround just import your MCE Clip into a VSE via Add (Shift+A) - Clip - <Movie Clip Name> as it will produce the result you want in the MCE as well. The Frame Range used is the current Scene ones which is applied to both the VSE and the MCE. You could delete your VSE Strip of the MCE clip afterwards if you don't want it to be rendered out.
When your MCE is open, you could just use this line of Python to achieve your goal:
bpy.context.scene.frame_end = [area for area in bpy.data.screens.get(bpy.context.screen.name).areas.values() if area.type == 'CLIP_EDITOR'].spaces.clip.frame_duration
This basically just sets your End Frame to the Length of your Video Clip that is currently loaded into your MCE. It does so by getting the current active Screen, searching for the Area which is the MCE and uses this only one left from the list of all visible areas and from within it takes the selected/active clip and uses its length.
Paste it into a Python Console View, hit Enter et voilà.
And I already described how to execute such a piece of code via hotkey.