Can I merge my Facebook page with another page with the same name but who's admin is not my friend and neither do I know him/her? If yes, then how?
Yes. You could merge the links as long as the names are same. Content on the Page with more likes will remain unchanged, except for the addition of likes and check-ins added from the Page with fewer likes.
Check this out (official FB doc): https://www.facebook.com/help/249601088403018/
I like this even better, it has screen shots
No, you cannot do this. The key part of this question is, "[The other page's] admin is not my friend and neither do I know him/her."
Notice that Facebook says, "Click the Merge duplicate Pages link. This link will only appear if you manage two Pages with similar names." Emphasis added.
The only way to merge pages is if you are the manager of both. There's nothing you can do (aside from reporting it to Facebook) about a page if you are not the manager.