As to your second question given only these details I can't answer but please try it.
Can I can connect HDMI cable from PC video card to HDMI jack on my TV and watch video from online?
Or should I use the router (somehow)?
I want to watch YouTube videos on my TV. My Roku model does not stream YouTube.
Will if affect my computer monitor as it is using the same video card - with the DVI connection?
Thanks for any info!