Merhaba.

I was wondering, what is this construction with "kadar" in the middle of a sentence, for instance:

Sevdiği kadar sevilmez insan; or
Gerçek olamayacak kadar güzeldi; or
Seninle başa çıkabilecek kadar kendimdeyim.

Could someone explain it, please? Thanks

"Kadar" has many meanings. 

Lets translate your sentences:

Sevdiği kadar sevilmez insan

A person isnt loved as much as he/she loves.

Gerçek olamayacak kadar güzeldi;

It was too beautiful to be true. 

Seninle başa çıkabilecek kadar kendimdeyim

I am conscious enough to deal with you.

Until an expert arrives to answer (*and I now see Gokuyum has beaten me to this answer), here are some things that might help

-diği kadar, -eceği kadar can often be translated to

´as ...... as´, ´as much as´, ´as long as´

eg Araba Soner´in istediği kadar büyük değil.

The car was not as big as Soner wanted.

So my attempt at explaining your second sentence is

Güzeldi = He/she/it was beautiful

Gerçek olmak = to come true (to be real)

Gerçek olamayacak = It could not be real

Gerçek olamayacak kadar güzeldi.

He/she/it was that beautiful that it couldn´t be real. 

Thank you for your answers!

There´s one more question left, are these sentences both correct?

"Hiç olmadıgım kadar güçlü" and
"Hiç olmadıgım kadar güçlüyüm" ?