Here is the second part of the discussion. Feel free to jump to the specific problem you are interested in.
Here is a timeline for your convenience:
Q5: 0:20
Q6: 19:00
Q7: 30:28
Erratum: In minute 11:30 I make an algebra mistake.
The value of X_0=(3/10)-(1/6)*(P1-P2)
After fixing this missed sign the best responses for each firm are:
P1=(9/10)+(1/2)*P2
P2=(21/10)+(1/2)*P1
Therefore, the equilibrium is not "weird", it is:
P1=2.6
P2=3.4
Apologies for the mistake :)