1) I am not sure if Tyflow support vertex animation bake, but I know there's some scripts that can do that automatically, and I also know old Joe Gunn tut of making that using 3DS Max standard cloth modifier (just ad the plane as cloth object, then go to sub levell, select all vertecies, make a group, and click on preserve. Hit simulate, and after it simulates, just click on "create keys"... and there you go.. you have edit poly mesh all animation baked to vetrecies
)
2) The travwel path of your particles you can achieve (I assume) in several ways.
Here's the 2 that cross my mind:
a) You just draw a line (in arc way) where particle needs to go, then use Path Follow operator to drive your particles from point A to point B (make sure your emitter is exactly at point A location). Also, keep in mind that path follow op is more like a force that will drive your patricles towards the spline, then really straight path on them.
Oh yeah, don't forget to add slow operator
b) You can try and sort off shoot out in a straight way from your Point A to point B, with speed operator... but also add inversed spherical wind (so it attracts particles), and in that way, you can, sort of create very organic looking arc ... I never did it with Tyflow yet, but I did it many times with PFlow.
Hope this helps.