SEO Juice

in my idea, nothing much different here :)

for me, i prefer 2nd
 
Ofcourse is the main domain . That is why most of the blogger looking for a new domain rather than using other subdomain which do not give much weight on SEO .
SEO more concern on the keywords in the main domain name.
 
It really depends on the situation. While the folder usually seems the best option, there are cases where you are better going with a subdomain.
 
If the content of the page is related to main domain, then chhose 2nd option, it will be the best
 
google has very clear guidelines on when and why sub domains should be used

http://www.mattcutts.com/blog/subdomains-and-subdirectories/

Sub domains should be used for content that is separate from your main site, such as news, affiliates or multi language/countries.

if it is just for general organisation of content then it would work best in a folder for SEO purposes.
 
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