I have had Home Depot cut countless boards and plywood for me over the years, so yes I would say they will.
I don’t see the option online to buy the whole bundle but I’m sure if you ask at the pro desk they can help you. I would advise caution if you buy a bundle since there are always warped or damaged boards in each bundle. But again, the pro desk can help you with informed decisions.
Have You considered asking Home Depot?
this wood is eastern white pine.
These should be sturdy enough for bed slats. I would choose these over the furring strips.