Do I need to request the owner's permission before using their infographic/YouTube video on my website post, if I credit them as source?
Most commercial uses of copyright works, and many non-commercial uses, require permission from the copyright owner.
Special licensing terms apply to YouTube videos:
If you have agreed to these terms, they will likely govern your use of YouTube videos and, even if you haven't, the licensing provisions will likely apply in respect of any acts that would otherwise infringe copyright. It is questionable, however, whether just embedding a video without permission is an infringing act:
To some extent the risks will depend upon the content of the video, which may be protected by independent rights (eg in audio or static images).
Similarly with infographics, you usually need some form of permission for copying/republication. Of course may infographics are provided in an embeddable form for the very purpose of promoting redistribution.
Apologies for the lack of a clear answer, but it really does depend upon exactly what you are doing with what.