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Subaru is renowned for their oil filter having a higher bypass pressure than standard aftermarket filters. IIRC, the OEM operates around 23 psi whereas most off-the-shelf are around 10-13 psi. Essentially, the OEM filter's bypass will operate less frequently, which means more oil will be going through the filter media. This seems like a big deal, but the psi rating on the filter is the differential across the media (i.e. it isn't triggered by the system oil pressure). Simply put, the bypass is a failsafe in case the media clogs, and since dirty oil is exponentially better than no oil at all, every oil filter on the market is manufactured with some sort of a bypass.
In theory, if your oil was clean and free of solids, your oil filter would never clog and therefore, it would make absolutely no difference what the bypass was set at. But that's not reality... we all get "gunk" in our oil to a certain degree; of course, that's why we have oil filters. Personally, I see no issue with using an aftermarket filter provided a) both the oil and filter are changed regularly, and b) you don't have any oil-related issues with the engine (e.g. excessive bits of metal/corrosion, carbon, etc. in the oil).
That said... there are two schools of thought on the matter: 1) the premium for OEM is worth it, even if it doesn't make a difference and 2) it makes very little difference whether you use the OEM filter or a quality, aftermarket filter. The overwhelming consensus, however, is that if you're still under warranty, you always use the OEM. But many Subaru owners report having used even the el cheapo Fram filters forever without any issues. For the record, that's what's on my Tribeca right now. YMMV.
As far as type of oil... frankly, anything that meets the OEM viscosity, ILSAC and API ratings is fine. Brand makes very little, if any, difference. Synthetic vs. conventional makes very little, if any, difference. (Again... provided regular changes of oil/filter.) Anyone who tells you otherwise is a sucker for marketing. For the record, I'm currently running the economy Shell conventional brand that I buy at Menards for $30/case when it goes on sale, and not only has my oil leak stopped, but I'm also burning less oil than when I was using Mobil 1 synthetic.
Unless the oil and/or filter hasn't been changed in a while - barring other oil-related issues with the engine - I wouldn't be too worried there; nevertheless, when buying a used car, the first thing anyone should do is change the oil/filter, even if the seller told you they just did a week prior. It doesn't hurt to change it now and see if the problem goes away... even if it doesn't help, you're going to have to change the oil at some point anyway (and probably should have already), so there's no "cost" to the slightest possibility that it is being caused by the oil/filter, which is, after all, a common link between the OSVs.