I own the same car.
The worst thing you can do to a JDM is a jugaar, that too with the cooling system. Have your radiator flushed and pour new coolant. As for the pick issue, my car had the same issue. Exact same issue. I had the catalytic converter removed and a new oxygen sensor installed. The car is amazing since then. My car's checklight lit up when I had the catalytic converter removed. Then, I had the oxygen sensor replaced and the checklight disappeared :). Get the fuel filter replaced aswell. Rest, just follow your routine maintenance. If you need anymore help, PM me. I've dealt with all sorts of issues I have this car since July 2013. The AC works well in the daytime during June/July. Don't expect anything extraordinary. It's a 12 year old car, bound to have some issues.