The vehicle in question is obviously misting (or puking) oil on hot exhaust components, hence smoke. Where? Nose and eyes will reveal the source tout de suite.
On the loss of coolant, lets hope its caused by something external, such as a hose or fitting. If it were internal, one might reasonably assume evidence at the exhaust pipe.
To the OP author: no offense but you sound a bit innocent in your evaluation skills. Please use caution when 'trusting' the troubleshooting/repair recommendations of a shop - any shop, whether Honda stealership or independent. As I'm sure you are aware, both are known to serve their best interests (meaning max_$) and tend to prey on the less-than-well-informed.
At your mileage, it may be time for a general refresh in the plumbing department. PS hoses, rad hoses, trans fluid, ETC.
Ask questions here, lotsa helpful folk around these parts. Best of luck!