yes there is a gasket around the thermostat. If your thermostat hasnt been out for many years its probably a good idea to replace it. Only like $3 for a new rubber o-ring gasket.

If you fill it up from cold and idle for 10 mins it probably wont over heat. But keep an eye on it anyway

You want to cycle the flush solution as much as possible so burb and bleed the system of air with the flush solution in it so that it cleans the whole system properly not just the block.

Then drain and re-fill again with fresh coolant.

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RS Liberty - Because WRX's are only good for parts...