Do all engines hyundai engines warble?
 

I'm noticing my engine on my 5 speed sounds like it warbles(that is the best way to describe it using words) as I accelerate. It doesn't seem smooth, is that normal?
Well, I guess that is hyundai smooth but is that normal?
350km on car so far._

Well, the Beta II engine in the Touring is an older design. Not nearly as smooth as the more modern Theta and Gamma 4 cylinders.

I have just found out my rad fan is not working. The engine bay got real hot, the battery got too hot to touch. I have driven it a total of 350 km short hops. Hopfully there hasn't been any engine damage. I am contacting the dealer tomorrow about it. What sort of short / long term damage will this have done to my engine? What should hyundai do besides just fix the problem?

If the warning lights didn't go on and the temp gauge wasn't in the red, you probably didn't do any damage.

There should be an engine check to let you know it's working properly. I'm almost surprised cars can't tell you something isn't functioning.

Shouldn't I be worried about warping the cylinder head? At least nothing boiled over.

I am almost certain the fan should come on after 5 minutes of driving and pulling over and letting it idle. I do not want to let it idle for too long just to see it doesn't come on and do maybe more heat damage.

Also oil change stick has 2 tone color to it like it's gotten really hot and the metal has changed color due to the temperature.

The engine check is the temp gage and the warning light, both are there to tell you how the engine cooling system is working. During normal driving your fan rarely runs, just the moving air thru the radatior will keep the cooling system cool enough. The fan gets more use in heavy stop and go traffic.

Watch your temp gage, It should get to a certain point, (my car the gage stops just below halfway) and stop there, even if the fan isn't working it will stay at that point for a little while before the gage will start to rise again. If it gonna peg and you will know if it is. pull over shut it off and call the dealer. A moving car will decrease the rate it pegs.

Update, so far so good. Yay! (knock on wood) The temp gauge goes just below halfway and doesn't budge from there. The oil dipstick is normal like that two tone for hyundai.

From the dealer already having 24km on it new (to tint shop and back) means someone who may or may not have been competent enough driving manual transmission may have taken it for a test drive and really wound the heck out of it .. who would really know, it was off the dealer lot for a few days. But I'm getting better than average fuel mileage ( 6.6 L/100km 36 mph ) so maybe that was a good thing. Who really knows. But things seem to be in order and appear to be working okay, let's hope it turns out to be a long lasting car.