Hey there,

I am really sorry for the delay of this reply as it is a weekend for us here.

1. How can I publish an ES Search module in ES's default left-side module position of Pages section, pricesly just above the default Pages module?

Are you referring single Page layout or page listing layout?
Perhaps you can try turn on this setting "preview module position" setting from your backend template configuration setting. (screenshot : http://take.ms/N0spc )

Once you turn it on, you can access your page and append this ?tp=1 on your page URL.
For example : domain.com/index.php/community/pages/1-super-page?tp=1
So it will show up those module position name on the page.

2. When I use ES Search in Pages section, is there any way to dedicate the module only to search in pages, closing other search options like groups, peoples, etc?

Unfortunately currently that was not possible to achieve this.