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The videos that are taken using the front-facing camera are saved with flipped images. Is there any way to change this? Thank you.
I'll see if I can test this, but could you try settings > apps > all > camera > clear data > check again.
Usually that is the case with pictures, never recorded but @uliwooly can keep us updated.
I mean, I took video using primary camera (20.7mp) but after it looks like flipped now i was having hard time to rotate it.. 
Like a mirror image or upside down? if the later perhaps you are holding the phone wrong
yes, upside down 
You were holding the camera wrong, if on landscape the Sony branding has to be on the left side. You can use apps to rotate the video.