Do I need to change the CVT oil?

I would change it. The fluid is 6 years old. I would probably have a dealer do it but you can do it yourself if you like. Check youtube and the web for tutorials.

Well to make things more complex, I spoke to local Subaru dealership and they told me that for my make model and year, there is no need to change the CVT fluid. It is good for life and there is no requirement by Subaru to change it. But they do recommend to do it at about 150,000. Because there's always a buildup of little metal fragments and its good to get them out. (They did say to do the differential oil -front and back, at 60,000 though.)

Life means until it dies and they tend to die before 150,000 miles. The cost for a new CVT is around 8 grand.

Do you have an independent mechanic you trust? Take it to them and let them change your oil. I wouldn't wait until 150,000 miles. My 2010 has almost 105,000 miles and is perfectly fine. Your car is 8 years old, it will not hurt and mostly help you to do this. A lot has to do with how you drive. Stop and go traffic is much harder on vehicles and of course it also depends on where you live and the climate. Southern California is much easier on cars. By the way my independent mechanic tells me that there's plenty of places to get a replacement transmission for around $3,000. I wouldn't worry about the transmission assuming that you are not "racing" your car. I have heard that many people get well over 200,000 miles from their transmissions. Besides even if it fails, fixing your car is almost always less expensive than replacing the whole vehicle. And, you'll have to fix it anyway if you intend to sell it.