I got a simple digital receiver with can connect to an external harddisk for recording of ts-files.
Working with video can get complicated, in no small part because there are all sorts of variables that make/break compatibility with software &/or hardware devices. What your receiver does & what it records can have an awful lot to do with what works & doesn't, so as a 1st step I'd suggest starting there, using Google/Bing to research as necessary -- at the same time you might see what others with the same hardware use, potentially cutting out a lot of research &/or trial & error. Having TS files means little, since they can hold a dizzying variety of formats/content. Once you know what you have to work with, targeted searches give better results, & you can also post specific problems/questions in forums like videohelp & get decent, targeted replies.
simple ts-file editor that can cut the length of a ts-file - and maybe (optional) split/divide that file
Mjpeg, DV, & even mpg2 with the right settings are examples of formats where every video frame is a complete, stand-alone image -- these types of files can be cut &/or spliced anywhere, with a new file written without re-encoding anything. Varieties of mpg4 OTOH &/or the mpg2 on a DVD or Blu-Ray have each full frame followed by several that are incomplete, recording only the changes between complete frames -- trimming, cutting, &/or splicing might involve re-encoding only at edits, may only be possible at complete frames, or may be impossible without a complete re-encode for a particular format. You're also more limited when choosing an editor for those video formats with incomplete frames, since that editor has to build each frame into a complete picture for preview, & not every editor will accept every format out-of-the-box -- in some cases you might have to convert to an intermediary file, edit, & then re-encode.
why my standalone LG HD-recorder is able to do the same cut in just a few seconds
Again, Google/Bing to find out what exactly it's doing. If your recorder does a trim in a few seconds, it's probably not altering the recorded file at all, but simply changing its internal direction set to say start playing this file here, stop playing there. DVD recorders can use a similar trick, where every recording is divided up into many, many chapters, & directions to the player amount to a list of just which chapters to play. For DVDs you can use the same trick in software.
For a decent list of video editors visit the Tools page at videohelp.com.