Lovely ride.
Adnan,the hose pipe looks ok not that bad in shap.
If this car had an over heating history,tappet and head joint will tell you story if you keenly look around it and find some spot with local silicon,or a bit extra thick head gasket would obviously be visible by its gaps,you can compare these points with a new car,this is absolutely myth upon observing a hose pipe one is making a wrong belief.
At safer side,use the coolants not just tap water,coolants will give you some benefits in the long run,coolants better shields your car because they boil way beyond 100 degree whereas water at 100,antifreeze/coolant are of a high quality concentrated ethylene glycol based liquids,Antifreeze/coolants helps protect the cooling system against freezing and corrosion as well, thus offering excellent cooling in the summer as well as protection against winter freeze-up though later part is not applicable in most of our cities.The use of de-ionized water ensures that no hard water performance detriments are introduced in premixed coolans as i use personally korea's GS coolant cost 160'500 ml.
