Creative

You can indeed split the RF feed coming out of the STB. I would split the RF feed, feed one feed into your normal equipment (TV whatever) and the second feed I would amplify before sending it on its longer run. You could amplify directly the output of the STB before splitting it if the normal equipments feed is affected too much.
As for splitting baseband video, it really depends upon run length. The equipment is designed to have an impedance match at 75ohms. When you start splitting video you change the impedance and video can look washed out as a result. The run lengths you will get won't be particularly good either. A video sender would be better I would have thought.