The SD STB box does not provide a HD picture. So you will see SD picture from SD channels (or blurry). If you have a QAM tuner in the new TV you can get HD on unencrypted channels (local channels) if you remove the STB. I've tested it and it works. Now how can you switch back to the SD STB to see the encrypted channels is the question.
Yes, but you will only get SD quality picture.
So if it is a large TV and it is stretching the picture to fill the screen, it may appear blurry.