SEO for mutilanguage site

How does exactly SEO work with multilanguage site?

1. Do I need to backlink www.mydomain.com/en/ or root domain www.mydomain.com ?
2. How page PA and PR builds up? Again is it for root domain?

Is having multiple domains for each language is more beneficial than having one?

And is multilanguage website SEO done any different than single language sites?

No. Multi-language websites have same SEO. You may add backlinks from different language sites. But links from same site will be more beneficiary.
So focus should be on getting links from same language websites.

Your URL structure should reflect the languages you're using. You can have one of these structures:
http://www.example.com/en/, http://www.example.com/es/
http://www.example.com, es.example.com
example.com, example.es
Then, you should "interlink" your pages with the hreflang attribute of the link tag. Assuming, you chose version 2 for your URL structure, then on every(!) page on your site, you have to point to all the appropriate pages written in your other languages. Including the page itself. An example: Every "page-1" has to have these three hreflang notations to tell Google that there is another language version of that very page.

Google will treat your site as one site, not matter wether it's split across several subdomains or even domains. Of course you'll do better for example in Spain when you get a lot of links from Spanish sites. But even without having any Spanish link, with the help of hreflang you'll get rankings in Spain, when your main (e.g. English) domain has a lot of links. Of course you can maintain different sites (on different domains) for different languages without interconnecting them via hreflang. But then you have to build links for every domain.

Here's how the hreflang tags look like:
<link rel="alternate" hreflang="es" href="http://es.example.com/page-1" />
<link rel="alternate" hreflang="en" href="http://www.example.com/page-1" />
<link rel="alternate" hreflang="x-default" href="http://www.example.com/page-1" />

(The forum software forced me to split this post ..)