Is Serial Numbers enough to make sure that my macbook is a brand-new one and really made by Apple?

Why do you suspect it isn't?

Do a google search for "apple serial numbers". Among the hits you will find sites that can decode the number or just tell you how to do it yourself.

Note, many of those google hits keep referring to this site.

depends... did you get it from a reputable retailer? even certain retailers could fall through loop holes...

...there's no way a consumer can really tell regardless of sites claiming they can decifer the serials...

You may find this link useful:

http://support.apple.com/kb/HT4132

Ciao.