I'm replacing a White-Rodgers thermostat with a new programmable Honeywell at my mom's (she has a heat pump). The original wiring was as follows:

Green=G, Yellow=Y, Red=R, White=W2, Blue=X1, Orange=O, Brown=E

The slots on the new on are (left to right): B-O-G-Y-W-DO NOT USE-R-RC.

Assuming everything that matches goes back in the same letter's slot, where do the Blue and White wires go? Also, do I need to put a jumper between the Yellow and White wires? She does not have a backup/alternative source.

The X1 blue wire is the common, you new stat doesn't need a common. Cap off blue wire. White wire will go to W. The R and RC should have a jumper between them. Then land your Red wire on R or RC.