You can use Okular, of course: print to file -> the pages you want. But thus you get an image pdf. If you want keep a text pdf, you can use a program like PdfArranger, which allows to save (only) the pages you want from a whole pdf, keeping them as searchable pdf (text).
Correcting subtitles framerate may be very important to sync it with audio/video. You can select all subtitles with an editor, and change framerate (for example to 25 from 23.976).
Thereby you should see the video correctly (with VLC or others).