Slitherine

HF (with HW) breaks HF after melee and wishes not to pursue. Under 13-12 page 107 "an unbroken battle group, all of whose close combat opponents (except only fighting it as an overlap) have broken and routed this phase, always pursues (even if it only fought as an overlap). In this case the winning HF was matched up 3 bases of frontage to 3 bases of enemy, but was in base to base contact on each side edge with friendly BG still in base to base contact with enemy.

1) Does winning BG have the option to pursue? Or must it stay and fight as over lap on each side?
2) If winning BG has option to pursue, can it take a CMT not to pursue? It is HF Pike. IF HF HW does this make any difference?

On Page 108, it state that "Initial pursuits obey the same rules as pursuits in the joint action phase for moving multiple battle groups, FOLLOWING ROUTERS...

Moving to the joint action phase portion of the rules, on page 115, it states "Pursuers who remain in contact with routers must pursue unless they pass a CMT to STOP pursuit."

Since, according to the Full Turn Sequence on page 179, under Melee Phase, Initial Rout Moves are completed before the Joint Action Phase, the question is do pursuers have to pursue at lease one turn before they can take a CMT to stop, unless page 107 allows them not to pursue in certain cases, such as HF with HW not having to pursue mounted?

Clarity, Please!

Unless one of the exceptions on page 108 applies pursuers have to pursue at least once (in the melee phase).
The fact that you fought only as an overlap does not prevent you from pursuing.

If your frontal opponents did NOT break and rout but their friends who fought you only as an overlap did break and rout, you do NOT pursue the routing enemy bg (because you are still in frontal contact with an unbroken enemy).

1) Does winning BG have the option to pursue? Or must it stay and fight as over lap on each side?

No - pursuit is compulsory.

2) If winning BG has option to pursue, can it take a CMT not to pursue? It is HF Pike. IF HF HW does this make any difference?

If vs foot - all must pursue. If vs mounted - shock foot must pursue unless they pass a CMT not to. Non-shock foot must pass a CMT to pursue mounted.