Recently my xbox couldn't detect my router anymore and through many tests I concluded that the signal was somehow now too weak. Do you think that this guide http://www.dslreports.com/faq/12506 would help me improve my wireless signal if I use the secondary router for wireless?
Yes, an extra wireless router can help if you're not getting good coverage throughout your house.
Before adding a Wireless Access Point (WAP), you might try changing the wireless channel. It could be that there is now some interference on the current wireless channel.