Do I have to add also a 10k (or other value) for that pin like in that configuration above, to avoid a short cut on PIC core, or can i direct connect the wire?
Looking at the SP0256 spec you sent, this is a 5v device just like the PIC core. The LRQ output can drive 2 LS-TTL loads with a ZERO voltage of 0.5v and a ONE voltage at 2.5 volts. The PIC running on a 5 volt power supply can input a ZERO for anything less than 0.8v and a ONE for anything over 2.0 volts. So you can directly connect any of the SP0256 outputs to the PIC inputs without any issues. No resistor necessary.
When you are debugging your code I would remove the SP0256 from the socket and make sure that your software has configured the TRIS registers correctly. You don’t want to drive one of the SP0256 outputs with outputs from the PIC. You might blow up your SP0256 output pin if your PIC is configured wrong.