Hi - the small diameter pieces,I would leave them as long as convenient,seal the ends,and leave them to dry somewhere covered but out of direct sunlight,if possible.
What do you think you want to make from the trunk section ? The very least you need to do is try to split it lengthways through the pith and seal the ends.Would be better if you can slab/plank it 2 to 3" thick,then stack and sticker it.Bowl blanks are normally cut from planks (side grain) so this leaves your options open on final use.
If you want to cut them to smaller sizes for convenience of handling,for later use as bowl blanks,make them slightly longer than the width,to allow for trimming the ends incase of any end splits/shakes.
As with all things,this isn't the only way of dealing with it,but hopefully wil give you some ideas.
Andrew