I am not sure of the wood, but the markings are spalting.
Plenty of threads on this forum about sealing wood.
Examples of sealing options :
a) Anchorseal
b) Paraffin wax
c) Paint (not good for the tools, but will seal the wood).
You should either seal the wood for turning later, or rough turn to whatever shape you want, then put aside in an area with no direct sun and low air movement.
If the wood has checked, try to avoid that area, or you may need to try CA glue to stabilize.
If you seal it will not dry, which is the intent of sealing.
If you turn to a rough i.e. thicker wall than desired, but the shape of the desired form, the period to dry depends on the wood (amount of bound water in the cells), the wall thickness and the moisture content of your area.
You either need to weigh the pieces each week and note the weight, or get an inexpensive moisture meter and measure each week. It will be a 3 - 6 months before it reaches equilibrium with your shop/storage location.
I have this one, note the Lowes description is wrong. This is a moisture meter not temperature meter.
http://www.lowes.com/pd_78059-56005-MMD4E_0__