Yes. The embed code is necessary in order to show a Zigpoll on your website.
The embed code needs to be on any page where you want to show a Zigpoll. If you don't want a poll on the page, you do not need to include the embed code on that page.
You should place the embed code in between the <head> tag at the top of your website. You can also include it before the closing <body> tag if you prefer.
Yes. Check out this link: