#1
Ok I am wondering if there is an easy way to derive other scale shapes without having to memorize the fingering.

So say I memorized the 5th position of C Major and I want to improvise on D Major, I want to know how to change the shape relative to the familiar C maj 5th position shape

I know one note changes every time you go up a fifth, is there a logical way of knowing what this note is?

For example when going from C maj to G maj the F turns into an F#, but so far the only way for me to know this is by looking it up and memorizing it.

Do I really have to memorize all the whole and half step pattern for all the modes, I am super lazy.
#2
Well since no one else has replied I'll take my best shot. I never really bothered with learning the Co5ths, per se, but I would venture to guess that the 4th (in your example F) of the original key (C) moves up one to become the major 7th (F#) of the 5th you are changing to (G). Check this yourself to make sure this is right as I am lazy as well.
Stop whining and learn your theory!

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Yeah, some black guy with a yankees cap walks into the ice cream parlor, and I said "We dont serve your kind here," as in, yankee fans, i guess he thought something else and left.