I'll post my opinions for Q1. Check to see if there's any problem...

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Consider the configuration

. Without loss of generality, let

. Let

(otherwise no feasible plan exists).

Conjecture: Let the motorcycle go straight to

and carry him forward to catch

. A feasible plan exists

*if and only if *the motorcycle is able to catch

before or

just when she reaches Y.

If the motorcycle **just** catches ; by that time A3 has already finished the journey since,
Is the above conjecture true?

If it is, then

looks like this:

={

}.

An illustration is given below for m=10. For any m, just shift the the blue lines up or down.