learning language

Is an I move like an incremental move?

If so add the INC option to the end of a move, and then populate the position with how far you want the robot to move.

Sure, see example below.

/PROG  INCMOVE
/MN
   1:  UFRAME_NUM=0 ;
   2:  UTOOL_NUM=9 ;
   3:J P[1] 10% FINE    ;
   4:L P[2] 250mm/sec FINE INC    ;
   5: !TCP now at 1525 Y ;
   6:L P[2] 250mm/sec FINE INC    ;
   7: !TCP now at 1550 Y ;
   8:L P[2] 250mm/sec FINE INC    ;
   9: !TCP now at 1575 Y ;
  /POS
P[1]{
   GP1:
	UF : 0, UT : 9,		CONFIG : 'N U T, 0, 0, 0',
	X =     0.000  mm,	Y =  1500.000  mm,	Z =  -350.000 mm,
	W =     0.000 deg,	P =     0.000 deg,	R =    90.000 deg
};
P[2]{
   GP1:
	UF : 0, UT : 9,		CONFIG : 'N D B, 0, 0, 0',
	X =     0.000  mm,	Y =    25.000  mm,	Z =     0.000  mm,
	W =     0.000 deg,	P =     0.000 deg,	R =     0.000 deg
};
/END

UTOOL is which TCP to use. In the case of the above, use the 9th programed TCP.
UFRAME is which user frame to use. A UFRAME of 0 is the world frame.

For wrist configuration, and turn numbers, watch my YouTube video on the subject here.

The reason you are getting uninitialized errors is that the Fanuc controller uninitializes the point data when the INC command is added, for safety reasons. You have to go in the point and type your incremental offset in.

Wrist configuration is ignored in INC moves. I am not sure about turn numbers, you will have to experiment with that one.

When you record a position the UFRAME and Tool Number are also stored along with the posture configuration
Depending on a variable setting the robot will automatically change the current tool frame and user frame
It is usually disable, so you MUST include the UTOOL and UFRAME instructions to set the correct frames, otherwise will give you an error

About the posture configuration, in general (for articulated type robot manipulators) there are 8 possible solutions for a given position
wrist Flip, No flip
Elbow Up, Down
Arm fronT, Back
The combinations (2*2*2) give you the 8 possible solutions, of course depending on the position some solutions are not reachable

That should work. What are you specifically trying to do?

Instead of incremental, why not just use a PR offset set to the increment you want to move. Then replace line 3 with:

3: L PR[12] 100mm/sec fine Offset, PR[13]

Also modify anywhere P[4] was used, such as in line 9.

They go over something similar in this thread. Maybe that will help you out.

The Tool Frame tells the robot where the tool center point is for the End Effector that is installed on the robot flange. Tool Definition is another way to describe it. You define the point where the robot actually rotates around when you are jogging and also which direction the X,Y,& Z are for the tool. You can then use a TOOL OFFSET in the move command to offset the point in the direction the tool is pointing, instead of offsetting relative to the WORLD coordinate system. The tool frame is basically the frame of reference like you said, which moves around with the robot flange.

Quote

J P [1] 50% FINE with a TOOL_OFFSET,PR[X]

If you use the motion modifier "Tool Offset, PR[X], then that is all you need to do. You do not have to set up a condition. It will use whatever the currently active tool frame is and offset by the value in PR[X]. Keep in mind the offset will be from the UTOOL orientation.

To better understand what the outcome will be, just create a little test program with the robot moving in empty space with some different tool offsets applied.