Burning oil and clicking....,,,
Clicking noise on a cold start is usually the hydraulic valve tappets - light clatter before the oil gets pumped up to them......5 or 6 seconds. Only usually noticeable after the car has been standing (say) overnight. Means?......a little bit of wear creeping in and the small amount of oil retained in each of them starts to weep out over time, (welcome to the club :-) ), but might not become an issue for many, many 1000s miles...........keep up oil changes and don't rev too high for first few seconds of running (i.e. until clattering stops).
Oil leak / burning smell - could be a number of things but if its happened suddenly AND you're starting to get leaks all over the place, then try investigating the crankcase breather plumbing. If this gets blocked, the crankcase will pressurise above normal and 'blow' oil out of anywhere it can.
Not necessarily the case in your case but I have had some 'miraculous' fixes for 'orrible oily engines on many makes by clearing the breather system out......usually it must be said on higher mileage cars.
best of luck,