If Xerath uses Rite of the Arcane (R) and Ahri charms him, will he move, or stay in the same spot?
If Xerath gets foced to move, the ability will be interrupted and he will move. This counts for Ahri charm, fears (Fiddle Q etc.), knockups (Alistar Q etc.) and knockbacks (3rd Riven Q etc.). Normal stuns, roots or silences won't end the Locus but you are unable to cast spells or autoattack while stunned/silenced.
Also if this stance gets interrupted the Bonus movementspeed will not be granted.
There was also a discussion on the forum to make xerath immune to CC that forces him to move, but he's getting a rework now anyways where they replace the W with another spell.
Lol wiki seems to state that
A champion that roots itself is unable to control its movement and will ignore movement commands (included forced actions, such as fear). A champion that is rooted can still be moved by airborne effects, but it will not break the root.
I will try to test this in the near future
Xerath wouldn't move, because he is effectively snared or root himself, which prevents movement except for knockups. I believe Riot did this so that you couldn't be snared and pulled it to prevent you to escape, but if you timed them right, it will effectively do it.
As of Xerath's recent rework the Wiki states:
Interrupting crowd control effects, with the exception of displacement effects, will interrupt Rite of the Arcane and put it on full cooldown.
As Ahri's charm is an interrupting cc effect, it will end Rite of the Arcane and put it on full CD.