DES F function never injective? Now i know that the F function doesn't have to be injective, but is it NEVER injective? or is it possible to have an injective F function?
There is nothing that stops a Feistel cipher from having injective Sboxes.

One could remove the $32$ to $48$ bit expansion map $E$ in the DES $F-$function and have an injective Sbox layer made up of $4\times4$ Sboxes and thus an injective $F-$ function for a modified DES. It would need round keys of $32$ bits and thus use less randomness and be weaker.

Also, there are many Feistel and generalized Feistel ciphers out there, including AES finalists MARS and RC5. Studying them may help you understand $F-$ function design better.