Doghairs you definitely want to choose your FP selections from home if you can, especially if you're visiting at a busy time. That way you will get the best choice and some FPs run out very quickly so they may be gone by the time you get to the park. Also it just wastes time to queue in the parks to use the FP machines there.
Bacon, you might want to change FPs when you're there if your plans change. For example, last time I booked FPs from home - the first one was at 10am but on the day we couldn't make it there that early so, rather than lose the FP, I was able to change it to a later time. Or sometimes we decided to visit a different park instead, so swapped FPs to a different day.
The Child Swap thing is for if you have a child that is too small/doesn't want to ride, both parents can ride without having to queue twice. Parent 1 queues for the ride as normal whilst Parent 2 waits somewhere else with the child. Parent 1 comes off the ride and waits with the child and Parent 2 can then go straight onto the ride without queueing. The arrangements are slightly different at each ride (sometimes you get a Child Swap ticket, sometimes you wait at the ride exit) - just tell the staff memeber on the entrance that you want to child swap. If you have other children in the party who DO want to ride, they can go with each parents ie. they get to ride twice :)