It's probably just "mayonnaising", as mentioned above. I get this on all my cars, because I often drive only a couple of miles at a time.
I had a head-gasket problem once (not a Peugeot). The indications were ... rust-coloured trails running down the engine block from the cylinder head, and evidence of mixing of the coolant and the oil. If you take out the dipstick it could show light-coloured bubbles in the oil, and oily/rusty deposits if you take off the cap from where you top up the coolant. Does the coolant or the oil need frequent topping up? If you can�t see any of these signs, there might not be anything to worry about, if the engine is running OK.
The flashing warning lights I don�t know about.