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ummmm, even if that TV is working live on the computer from website?
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You should be able to save the stream some how. The software would need to be designed for that particular type of live TV. Additionally if you can download the programs (like from BBC Iplayer) you might be able to strip them of their DRM and then edit them as normal movie files.
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like lets how, how to capture whatever sound and vid the is going in my computer screen, is thAt possible?
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Yes and no. Simple screen capture programs like those used for video games would work but unless the screen resolution is of that of the native video stream you will get a loss in quality. Additionally many video sources such as full quality Blu-ray and possibly streaming programs will use a secure video playback feature built into your graphic hardware itself to prevent you from being able to record the resulting image stream (damn DRM).