Engine very noisy while running and on start car can go down.

noisy on start up is hydraulic lifter problem as they are loose until the oil pressure builds up. the adjustment is taken up and the noise goes
it mat have some noise from the chain until the oil pressure builds up as it has a hydraulic chain tensioner
you list it as a 2016 model and the only suggestion I could make is to go up a grade in oil viscosity
AS it is new the oil is probably 15w where I would use a 20 w 40 oil
run your engine against other new engines and see if the engine noise is louder ( use a noise meter ) and make the dealer do something as nothing gets quieter as it wears out --just louder

A tapping noise that starts out cold and goes away when warm is usually caused by a valve lifter inside the engine. The lifter may be worn/leaking down and will be noisy until it fills with oil pressure. You can try an oil additive ( Lucas Oil Additive ) available at most part stores works very well with noisy lifters. Another noise that can happen cold and go away when warm is an exhaust manifold leak. However, this is normally a ticking type sound rather than a tapping sound.

It may be worn out valve lifters that are inside the engine. If you have more than 6,000 miles on the oil, valve lifters could run noisier. Changing to a high mileage type of motor oil may quite down the valve lifters noise somewhat. Synthetic oil used during the summer months could make it noisier too. If you can hear the noise while driving the car, it is not normal. Upon acceleration, if it gets noisier, you will be needing a valve job in the not to distant future.

You can find the vacuum leak easily. With engine running, spray some starting fluid near where you suspect the leak to be. If the engine speeds up from sucking the starting fluid in at the leak, you found the leak. Fix it. As for the burning oil and engine noisy, you will need to rebuild or replace the engine because it's worn out.

it depends. we need to know a lot more like:
-oil weight used
-when does it happen (morning,afternoon)
-does it happen when hot or cold
-are you driving it offroad

if you had a shortblock replaced at 8000km that tells me something about YOUR driving habits and how you maintain a vehicle

Have you tried flushing the engine crank case? You may have sludge clogging the valve lifter oil pressure ports. Get a can of Berrymans brand Chemtool, add it to a cold engine crankcase oil and run it for 5 miles or so, then change the oil and see if the noise level improves. Some tapping noise on cold start is normal and not a sign of any problem. If the noise goes away in my opinion I'd just do the flush of the system and then leave it alone.

The fuel pump is supposed to run constantly when the engine is running. It is pumping fuel to the engine which is in constant need of fuel. It is starting when the ignition is turned on and then shuts down after a few seconds if you do not start the engine. This is exactly what it is supposed to do. You have no problem except for the pump being noisy. On a car that is 22 years old, I would suspect the fuel pump is failing and the noise you hear is it's death nil. Change the fuel filter and if the noise continues be prepared to have the pump replaced. It may fail suddenly or it may become hard to start. If you have never had it replaced just go ahead and do so, to prevent being stranded and a towing fee when it does fail.

If you think it's the timing belt, get it replaced or inspected.

Even though there are other things that might make a noise, the damage you might do by having the timing belt fail while the engine is running are not worth the risk.

Look for water pump, fan belts, steering belt, AC belts and pulleys. These are common causes of these strange noises which come on and off. Also check all the mechanical nuts, bolts, screws are tightened and not rattled.