As in topic. Let's say I recorded clip in faithful picture style, can I change (like using DPP on stils) picture style for enitre video after is done? Maybe easy questions but complete new for me. Thanks

Can't I'm afraid. The camera does not store the raw data when shooting video. Instead, each frame is compressed and encoded to H264 according to the selected picture style.

You can do a certain amount in post with the footage, but there is no alternative to getting the picture style right first time.

Yup, the answer is no. You can only choose a picture style afterward if you shot RAW (stills) but if you shoot jpeg the choosen picture style is applied immidately. Think of the .mov being your jpeg in video mode. The camera doesn´t record raw video as already mentioned.