In case of pronuncing "support you", I thougt connecting 't' to 'y' makes a 'ʧ' sound, so that It's sound like "səˈpɔːrtʃu". but I found many videos in which It's sounded like "səˈpɔːr u". Which pronunciation is correct? Are both correct? Is there standard of pronunciation on this case?
It does indeed sound as if the letter "t" is swallowed, in many cases. However not everyone speaks like that. Some people pronounce the letter "t" and pronounce the word "you" apart from whatever comes before it. Others may speak differently.
In many cases it depends on the region or the country since the English pronunciations differ and vary much across the planet.
There isn't a strict rule to what should the correct pronunciation be. My advice would be to choose one that you like most and work on it. I prefer to slightly point out the "t", so that it sounds dull, and emphasise the "you".
You can always go by whatever pronunciation you prefer most.