A swingaxle takes 2.8 pints if it's empty(new fill). Swepco is good, Amsoil, Redline also. There are others. Use 75w90 or 80w90. Buy 2 quarts, which is 4 pints.
I like conventional oils, they leak less. But some have had success with synthetics.
When doing a swing trans, I like to keep the wheels on the ground, it lets you fill it the way it will be run. The angle of the axle tubes matters for fill volume. They are usually angled up a few degrees.
I usually get it good and hot, then let it drain into a pan overnight. Refill the next day, don't forget to clean the magnetic drain plug before you replace. No sealant is needed, make it snug, don't overtighten.