Sources of white /grey / or blue smoke are :
1) Poorly sealing rings on the bore wall ie rings or bore worn out of round , honing peaks gone without rings bedding in ... bore wall or rings scratched or gouged by grit ... Rings can also be stretched out of round during installation or removal and they'll never ever seal again ... Even if rings are carefully removed from a bore ... the cylinder MUST be re-honed for them to re-seal to a high degree again ...
2) Ring end gaps too big ... Ring end gaps not properly staggered or in the wrong position in the bore ...
3) Oil can leak past worn , damaged or incorrectly installed valve stem oil seals ... the symptoms are usually a puff of white smoke on start up that goes away or diminishes as the engine warms up ... oil leaks into the ports while the engine is sitting ... but the leakage rate is too slow to make smoke while the engine is running ... The engine can puff white smoke when the throttle is backed off since the cylinder vacuum sucks hard on the seals when the slide is shut off ... The same can happen if the ring seal is bad too ... only the oil gets sucked up from the crank case ... Oil mist or smoke blowing out from the dipstick or vents can also indicate bad ring seal / blowby ...
3) Bore scuffed from over heating ... the rings expand , the ends butt tightly together , the ring keeps expanding and forces too hard on the bore scraping the honing off and glazing the bore ... then when the engine cools , the bore is bigger than the rings ... it only has to be a micro thou bigger to be no good ...
4) Those junk thin steel shim gaskets that are supplied with some BBK's combined with the removal of the rubber O-ring and trumpet piece can allow oil to leak from the gallery into the bore ... Once again , the oil gets sucked into the cylinder on backing off the throttle from high revs ... Only copper or stock type gaskets which expand or crush unevenly can fill variances in between machined surfaces ... For a steel gasket to work , the machining would have to be perfect ... and that's pure fantasy without hand scraping and lapping each individual cylinder head to the cylinder ... They say to use Honda bond or some other type of hardening gasket cement , but anything like that can be blown out or crack and leak ... The very idea of using it to do the job of a head gasket is ridiculous ... and BODGEY ...
5) Even IF the parts were lapped to perfection ... the tensions of each cylinder stud would all have to be precisely the same and torqued in the proper sequence to avoid distortion ...
Bad ring seal or a blown head gasket causes smoking to get worse as the engine revs higher ... The colour varies from grey to white as the amount of oil getting burnt increases ... Only a rich fuel to air ratio burns black ...
The rattling sounds like he's done something wrong on re assembly ... ie cam chain loose , cam to crank timing out and valves getting clipped by the piston , rocker to valve stem clearances too big ... Not enough clearance can also cause a valve to hit the piston IF the valve to piston clearances aren't right ... A valve being held off the seat or a bent valve can cause a ticking noise as gas pressure escapes past the valve seats ... or a detonation type noise (rattling) in the exhaust pipe ...
Countless other factors can also cause weird noises or smoking ... A relo of mine told me that his XR75 was idling great after he rebuilt it ... then it suddenly locked dead while idling ... When he pulled it down he found the cam sprocket had broken in half ... The time before THAT the cam chain had "jumped" causing the valves to hit the piston and bend ... Obviously it was cracked from before ... So IF an engine fails on you ... thoroughly inspect EVERY part involved for hairline cracks ... no matter how minor you think the blow up was ...