Is it possible to have a bitcoin private key (hex) with 34 length? Something like 111111111111111111111111111ABcDE1f.
Private keys are always 256 bits long, that is 64 hexadecimals.
The printed string is usually longer then that because format labels and redundancy are added.

Anything shorter cannot itself be a private key, but may be used to derive one (preferably with stretching).

The string given looks too non-random to be used to derive a private key.

In general, 34 random hexadecimals are adequate to derive private keys.