Stabilizing is only necessary if you want to sweeten the wine when it's done. When it's completely done, you add 1 campden tablet per gallon and a small amount of sorbate (I'd have to look up the amount for a gallon, but it's like 2/3 tsp for 5 gallons) and rack the wine into it. After a few days, you can sweeten it as desired and no re-fermentation should start. Then you can bottle it. If you're not sweetening it, it's not necessary.
This is not a very gassy wine. You shouldn't need to degas it at all. Very few wines need to be degassed, usually only kit wines.
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