Yes, absolutely.
Possible failed valve cover gasket.Possible failed valve cover gasket.
No, if there is coolant in your valve cover it'll be mixed with oil. You blew your head gasket, possibly warped or cracked your head. It may look like coolant is leaking from your valve cover but it's your intake gasket leaking.
No
It can get in through the timing cover. That does car does not have a "timing belt" cover, but it has a "timing chain cover." There is a BIG difference, as a timing belt cover does not have coolant and oil running through it, but a timing chain cover does have both coolant and oil running through it.
Small pinhead size holes behind the water pump,eventually breakthrough the cover and voila you get coolant mixing with engine oil.
Mine is in the timing chain cover gasket. You can find your leak by pressure testing your coolant system.
The seal under the valve cover around the plug tube has failed.The seal under the valve cover around the plug tube has failed.
The thermostat is located on the side of the cylinder head, just above where the block mates with the head. There is a coolant inlet fitting (the thermostat cover) which should have a hose connected to it. If you can find that coolant inlet cover, the thermostat is located inside/under that cover. There should be two bolts holding that cover on.
Failed gasket.
On the lower left hand side of the motorcycle is a chrome plated plastic cover, this is right behind the clutch cable. You remove the three Allen screws with a wrench in your motorcycle tool kit. After removing the cover this reveals the coolant tank with the coolant levels embossed on the tank.
I would suspect a leaking water pump, if I remember correctly it is mounted right in front of the timing cover and if it is leaking from the back the water will find it's way out somehow.
below the coolant tank in a black cover.