From the picture it appears you don't have a VW Motorsport filter housing with the built in thermostat. The green wire is going to the OEM filter housing and is reading the Oil temp. It's hard to tell anything about the oil cooler except that you should replace the oil lines with a high pressure hose. If you use worm clamps on the ends instaed of AN fittings, use two. And check them frequently. Start up oil pressure can sometimes be close to 100lbs. The sandwich adaptor usually has arrows indicating the flow direction.
Also, if you again have restart problems check the fuel pump relay. Water gets into the fuse box and corrosion occures on the fuses.
Tony