Just on oil Coolers, Oil breakdown and excessive oxidation will take place above 130 degrees oil temp, generally hp is lost over 115 degrees, under hard driving an oil cooler is only recommended if the oil is regularly in excess of 120 degrees
Too cold oil is just a detrimental to an engine , wear and tear plus loss in power ; dropping oil temps down to 85 degrees will cost at least 1% hp
Unless you need one, you are causing yourself unnecessary trouble fitting one, if your temps are around 110-120 degress under normal driving conditions , you can still run at WOT for a few miles before temps become an issue
If you still want to fit one (With the help of Chris W) , it is best practice to to have the fittings at the top , and run an oil filter that has an anti drain back valve.
Reason remote mounted oil filters can be a bad idea, if you retain the stock oil filter position just off the side of the block, it will be in the best position for the anti drive back valve to keep the cooler and lines full of oil during long engine off periods. Then when you start the engine the pump doesn't have to refill all the lines and cooler before the engine bearings see oil pressure. Makes a HUGE difference to cold start wear and tear, and is just "good practice". Oil filter maker's sites will show if a particular filter has an anti drain back valve, or with a bit of experience you can look down the threaded mounting hole and see in many cases.
https://tpoparts.com/images/OilFilterCompare_4.png
The outer shell or housing
The spring, which seats the filter against the mounting plate
The filter core itself
The anti-drainback valve (this keeps oil inside the engine when the motorcycle is parked)
The mounting plate
The box
https://tpoparts.com/articles/oilfiltercompare.html