HelloCustomer first things first. If there is a gasket and a seal on top of the oil filter adapter, replace them both. Secondly, can you do it yourself. Absolutely. Take the filter off and visually you will see the bolts that hold it on. Remove it, clean the area, replace the seals and reassemble. It should take you less than an hour to do so. If that is leaking, that is a loss of oil pressure and that could be contributing to the leak. Replace them and you should be in good shape.
Your JA Expert,
Got it. Get every seal related to that cooler. Clean the lines and the engine thoroughly so you can spot if there is a crack in any of the components. Use brakeclean since it evaporates and will do a better job cleaning. After you replace everything, make sure the oil is full and have someone else start the car while you are underneath with a light, watching that area. Look for the first signs of any leak. If nothing, your done, If there's something, if you catch it straight away, you'll be able to locate it's origin.
You are absolutely on the right track.
There is one seal between the oil cooler and the bracket. You need a 27mm socket to take off the cooler- it has to be deep enough to fit over the threaded tube that the filter mounts to. The seal has a small tab on each side, that fits over the small posts on the back (upper) side of the oil cooler- you can mount it to any two of the posts, as long as they are directly across from each other.
The oil filter contains the other seal for this system, between the filter and the oil cooler- make sure when you replace filters that the old one doesn't get left behind stuck to the cooler, and lube the new filter with oil before putting it on. That is what makes this seal leak, filters get stuck on and when they are turned the oil cooler turns with the filter, loosening the nut.